Birational Geometry Of Hypersurfaces

Author : Andreas Hochenegger,Manfred Lehn,Paolo Stellari
Publisher : Springer Nature
Page : 297 pages
File Size : 44,9 Mb
Release : 2019-10-08
Category : Mathematics
ISBN : 9783030186388

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Birational Geometry of Hypersurfaces by Andreas Hochenegger,Manfred Lehn,Paolo Stellari Pdf

Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results. The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side. Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.

Author : Thomas E. Cecil,Patrick J. Ryan
Publisher : Springer
Page : 596 pages
File Size : 47,8 Mb
Release : 2015-10-30
Category : Mathematics
ISBN : 9781493932467

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Geometry of Hypersurfaces by Thomas E. Cecil,Patrick J. Ryan Pdf

This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hypersurfaces follows with results that are proved in the context of Lie sphere geometry as well as those that are obtained using standard methods of submanifold theory. Next comes a thorough treatment of the theory of real hypersurfaces in complex space forms. A central focus is a complete proof of the classification of Hopf hypersurfaces with constant principal curvatures due to Kimura and Berndt. The book concludes with the basic theory of real hypersurfaces in quaternionic space forms, including statements of the major classification results and directions for further research.

Author : Alexandru Dimca
Publisher : Springer Science & Business Media
Page : 277 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461244042

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Singularities and Topology of Hypersurfaces by Alexandru Dimca Pdf

Author : Daniel Huybrechts
Publisher : Cambridge University Press
Page : 462 pages
File Size : 50,5 Mb
Release : 2023-06-30
Category : Mathematics
ISBN : 9781009279994

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The Geometry of Cubic Hypersurfaces by Daniel Huybrechts Pdf

Cubic hypersurfaces are described by almost the simplest possible polynomial equations, yet their behaviour is rich enough to demonstrate many of the central challenges in algebraic geometry. With exercises and detailed references to the wider literature, this thorough text introduces cubic hypersurfaces and all the techniques needed to study them. The book starts by laying the foundations for the study of cubic hypersurfaces and of many other algebraic varieties, covering cohomology and Hodge theory of hypersurfaces, moduli spaces of those and Fano varieties of linear subspaces contained in hypersurfaces. The next three chapters examine the general machinery applied to cubic hypersurfaces of dimension two, three, and four. Finally, the author looks at cubic hypersurfaces from a categorical point of view and describes motivic features. Based on the author's lecture courses, this is an ideal text for graduate students as well as an invaluable reference for researchers in algebraic geometry.

Author : John P. D'Angelo
Publisher : Routledge
Page : 319 pages
File Size : 51,5 Mb
Release : 2019-07-16
Category : Mathematics
ISBN : 9781351416719

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Several Complex Variables and the Geometry of Real Hypersurfaces by John P. D'Angelo Pdf

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved). Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.

Author : Ivan Cheltsov,Ciro Ciliberto,Hubert Flenner,James McKernan,Yuri G. Prokhorov,Mikhail Zaidenberg
Publisher : Springer
Page : 509 pages
File Size : 52,7 Mb
Release : 2014-06-11
Category : Mathematics
ISBN : 9783319056814

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Automorphisms in Birational and Affine Geometry by Ivan Cheltsov,Ciro Ciliberto,Hubert Flenner,James McKernan,Yuri G. Prokhorov,Mikhail Zaidenberg Pdf

The main focus of this volume is on the problem of describing the automorphism groups of affine and projective varieties, a classical subject in algebraic geometry where, in both cases, the automorphism group is often infinite dimensional. The collection covers a wide range of topics and is intended for researchers in the fields of classical algebraic geometry and birational geometry (Cremona groups) as well as affine geometry with an emphasis on algebraic group actions and automorphism groups. It presents original research and surveys and provides a valuable overview of the current state of the art in these topics. Bringing together specialists from projective, birational algebraic geometry and affine and complex algebraic geometry, including Mori theory and algebraic group actions, this book is the result of ensuing talks and discussions from the conference “Groups of Automorphisms in Birational and Affine Geometry” held in October 2012, at the CIRM, Levico Terme, Italy. The talks at the conference highlighted the close connections between the above-mentioned areas and promoted the exchange of knowledge and methods from adjacent fields.

Author : Elisabetta Colombo,Barbara Fantechi,Paola Frediani,Donatella Iacono,Rita Pardini
Publisher : Springer Nature
Page : 200 pages
File Size : 48,5 Mb
Release : 2020-02-25
Category : Mathematics
ISBN : 9783030371142

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Birational Geometry and Moduli Spaces by Elisabetta Colombo,Barbara Fantechi,Paola Frediani,Donatella Iacono,Rita Pardini Pdf

This volume collects contributions from speakers at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the volume reflect the same idea, focusing on both these areas and their interaction. In particular, the book includes both surveys and original papers on irreducible holomorphic symplectic manifolds, Severi varieties, degenerations of Calabi-Yau varieties, uniruled threefolds, toric Fano threefolds, mirror symmetry, canonical bundle formula, the Lefschetz principle, birational transformations, and deformations of diagrams of algebras. The intention is to disseminate the knowledge of advanced results and key techniques used to solve open problems. The book is intended for all advanced graduate students and researchers interested in the new research frontiers of birational geometry and moduli spaces.

Author : Ivan Cheltsov,Jihun Park
Publisher : American Mathematical Soc.
Page : 117 pages
File Size : 40,5 Mb
Release : 2017-02-20
Category : Hypersurfaces
ISBN : 9781470423162

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Birationally Rigid Fano Threefold Hypersurfaces by Ivan Cheltsov,Jihun Park Pdf

The authors prove that every quasi-smooth weighted Fano threefold hypersurface in the 95 families of Fletcher and Reid is birationally rigid.

Author : Alessio Corti,Miles Reid
Publisher : Cambridge University Press
Page : 364 pages
File Size : 42,8 Mb
Release : 2000-07-27
Category : Mathematics
ISBN : 0521636418

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Explicit Birational Geometry of 3-folds by Alessio Corti,Miles Reid Pdf

This volume, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry.

Author : An-Min Li,Udo Simon,Guosong Zhao,Zejun Hu
Publisher : Walter de Gruyter GmbH & Co KG
Page : 376 pages
File Size : 55,8 Mb
Release : 2015-08-17
Category : Mathematics
ISBN : 9783110268898

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Global Affine Differential Geometry of Hypersurfaces by An-Min Li,Udo Simon,Guosong Zhao,Zejun Hu Pdf

This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry – as differential geometry in general – has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces. The second edition of this monograph leads the reader from introductory concepts to recent research. Since the publication of the first edition in 1993 there appeared important new contributions, like the solutions of two different affine Bernstein conjectures, due to Chern and Calabi, respectively. Moreover, a large subclass of hyperbolic affine spheres were classified in recent years, namely the locally strongly convex Blaschke hypersurfaces that have parallel cubic form with respect to the Levi-Civita connection of the Blaschke metric. The authors of this book present such results and new methods of proof.

Author : Joe Harris,JOE AUTOR HARRIS
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 42,5 Mb
Release : 1992-09-17
Category : Mathematics
ISBN : 9780387977164

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Algebraic Geometry by Joe Harris,JOE AUTOR HARRIS Pdf

This textbook is an introduction to algebraic geometry that emphasizes the classical roots of the subject, avoiding the technical details better treated with the most recent methods. It provides a basis for understanding the developments of the last half century which have put the subject on a radically new footing. Based on lectures given at Brown and Harvard, the book retains an informal style and stresses examples. Annotation copyright by Book News, Inc., Portland, OR

Author : Alessio Corti,Miles Reid
Publisher : Cambridge University Press
Page : 200 pages
File Size : 46,9 Mb
Release : 2000-07-27
Category : Mathematics
ISBN : 0521636418

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Explicit Birational Geometry of 3-folds by Alessio Corti,Miles Reid Pdf

This volume, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry.

Author : Janos Kollár,Shigefumi Mori
Publisher : Cambridge University Press
Page : 264 pages
File Size : 52,8 Mb
Release : 2008-02-04
Category : Mathematics
ISBN : 0521060222

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Birational Geometry of Algebraic Varieties by Janos Kollár,Shigefumi Mori Pdf

One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.

Author : John Willard Milnor
Publisher : Princeton University Press
Page : 136 pages
File Size : 40,7 Mb
Release : 1968
Category : Geometry, Algebraic
ISBN : 9780691080659

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Singular Points of Complex Hypersurfaces by John Willard Milnor Pdf

One of the greatest mathematicians of the twentieth century, John Milnor has made fundamental discoveries in diverse areas of mathematics, from topology and dynamical systems to algebraic K-theory. He is renowned as a master of mathematical exposition and his many books have become standard references in the field. Singular Points of Complex Hypersurfaces provides an incisive and authoritative study of the local behavior of a complex hypersurface V in Euclidean space at a singularity Z0.

Author : Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 41,5 Mb
Release : 2013-05-17
Category : Mathematics
ISBN : 9781461464822

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Birational Geometry, Rational Curves, and Arithmetic by Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel Pdf

​​​​This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.