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Author : Anthony A. Iarrobino
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 50,7 Mb
Release : 1977
Category : Mathematics
ISBN : 9780821821886
Author : Anthony Ayers Iarrobino
Publisher : Unknown
Page : 112 pages
File Size : 44,9 Mb
Release : 1977
Category : Hilbert schemes
ISBN : 1470400545
Author : Hwa Young Lee
Publisher : Unknown
Page : 164 pages
File Size : 48,9 Mb
Release : 2009
Category : Hilbert schemes
ISBN : UCR:31210022939761
Author : Zhenbo Qin
Publisher : American Mathematical Soc.
Page : 336 pages
File Size : 50,8 Mb
Release : 2018-02-26
Category : Hilbert schemes
ISBN : 9781470441883
Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes of collections of points (zero-dimensional subschemes) in a smooth algebraic surface . Schemes turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others. This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of , including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of and the Gromov–Witten correspondence. The last part of the book presents results about quantum cohomology of and related questions. The book is of interest to graduate students and researchers in algebraic geometry, representation theory, combinatorics, topology, number theory, and theoretical physics.
Author : Lothar Göttsche
Publisher : Springer
Page : 212 pages
File Size : 51,9 Mb
Release : 1994
Category : Mathematics
ISBN : STANFORD:36105008555836
In this book we study Hilbert schemes of zero-dimensional subschemes of smooth varieties and several related parameter varieties of interest in enumerative geometry. The main aim here is to describe their cohomology and Chow rings. Some enumerative applications are also given. The Weil conjectures are used to compute the Betti numbers of many of the varieties considered, thus also illustrating how this powerful tool can be applied. The book is essentially self-contained, assuming only a basic knowledge of algebraic geometry; it is intended both for graduate students and research mathematicians interested in Hilbert schemes, enumertive geometry and moduli spaces.
Author : Eduard Casas-Alvero,Gerald E. Welters,Sebastian Xambo-Descamps
Publisher : Springer
Page : 426 pages
File Size : 48,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540396437
Author : Lothar Göttsche
Publisher : Springer
Page : 207 pages
File Size : 53,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540483380
In this book we study Hilbert schemes of zero-dimensional subschemes of smooth varieties and several related parameter varieties of interest in enumerative geometry. The main aim here is to describe their cohomology and Chow rings. Some enumerative applications are also given. The Weil conjectures are used to compute the Betti numbers of many of the varieties considered, thus also illustrating how this powerful tool can be applied. The book is essentially self-contained, assuming only a basic knowledge of algebraic geometry; it is intended both for graduate students and research mathematicians interested in Hilbert schemes, enumertive geometry and moduli spaces.
Author : Hiraku Nakajima
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 48,5 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821819562
It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.
Author : Spencer Bloch,Charles Herbert Clemens,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 521 pages
File Size : 48,8 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821814802
Author : Andrea T. Ricolfi
Publisher : Springer Nature
Page : 310 pages
File Size : 49,8 Mb
Release : 2022-12-14
Category : Mathematics
ISBN : 9783031114991
This book is based on a series of lectures given by the author at SISSA, Trieste, within the PhD courses Techniques in enumerative geometry (2019) and Localisation in enumerative geometry (2021). The goal of this book is to provide a gentle introduction, aimed mainly at graduate students, to the fast-growing subject of enumerative geometry and, more specifically, counting invariants in algebraic geometry. In addition to the more advanced techniques explained and applied in full detail to concrete calculations, the book contains the proofs of several background results, important for the foundations of the theory. In this respect, this text is conceived for PhD students or research “beginners” in the field of enumerative geometry or related areas. This book can be read as an introduction to Hilbert schemes and Quot schemes on 3-folds but also as an introduction to localisation formulae in enumerative geometry. It is meant to be accessible without a strong background in algebraic geometry; however, three appendices (one on deformation theory, one on intersection theory, one on virtual fundamental classes) are meant to help the reader dive deeper into the main material of the book and to make the text itself as self-contained as possible.
Author : Anand P. Patel,Ashvin A. Swaminathan
Publisher : American Mathematical Society
Page : 114 pages
File Size : 54,6 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9781470461577
View the abstract.
Author : Francisco-Jesús Castro-Jiménez,David Bradley Massey,Bernard Teissier,Meral Tosun
Publisher : American Mathematical Soc.
Page : 217 pages
File Size : 40,6 Mb
Release : 2020-01-13
Category : Education
ISBN : 9781470447922
This volume contains the proceedings of the conference A Panorama on Singular Varieties, celebrating the 70th birthday of Lê Dũng Tráng, held from February 7–10, 2017, at the University of Seville, IMUS, Seville, Spain. The articles cover a wide range of topics in the study of singularities and should be of great value to graduate students and research faculty who have a basic background in the theory of singularities.
Author : Anthony Iarrobino,Vassil Kanev
Publisher : Springer
Page : 365 pages
File Size : 49,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540467076
This book treats the theory of representations of homogeneous polynomials as sums of powers of linear forms. The first two chapters are introductory, and focus on binary forms and Waring's problem. Then the author's recent work is presented mainly on the representation of forms in three or more variables as sums of powers of relatively few linear forms. The methods used are drawn from seemingly unrelated areas of commutative algebra and algebraic geometry, including the theories of determinantal varieties, of classifying spaces of Gorenstein-Artin algebras, and of Hilbert schemes of zero-dimensional subschemes. Of the many concrete examples given, some are calculated with the aid of the computer algebra program "Macaulay", illustrating the abstract material. The final chapter considers open problems. This book will be of interest to graduate students, beginning researchers, and seasoned specialists. Prerequisite is a basic knowledge of commutative algebra and algebraic geometry.
Author : Enrico Arbarello,Maurizio Cornalba,Phillip Griffiths
Publisher : Springer Science & Business Media
Page : 983 pages
File Size : 50,6 Mb
Release : 2011-03-10
Category : Mathematics
ISBN : 9783540693925
The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The approach is unique in its blending of algebro-geometric, complex analytic and topological/combinatorial methods. It treats important topics such as Teichmüller theory, the cellular decomposition of moduli and its consequences and the Witten conjecture. The careful and comprehensive presentation of the material is of value to students who wish to learn the subject and to experts as a reference source. The first volume appeared 1985 as vol. 267 of the same series.
Author : Piotr Pragacz
Publisher : European Mathematical Society
Page : 520 pages
File Size : 41,6 Mb
Release : 2012
Category : Geometry, Algebraic
ISBN : 3037191147
The articles in this volume are the outcome of the Impanga Conference on Algebraic Geometry in 2010 at the Banach Center in Bedlewo. The following spectrum of topics is covered: K3 surfaces and Enriques surfaces Prym varieties and their moduli invariants of singularities in birational geometry differential forms on singular spaces Minimal Model Program linear systems toric varieties Seshadri and packing constants equivariant cohomology Thom polynomials arithmetic questions The main purpose of the volume is to give comprehensive introductions to the above topics, starting from an elementary level and ending with a discussion of current research. The first four topics are represented by the notes from the mini courses held during the conference. In the articles, the reader will find classical results and methods, as well as modern ones. This book is addressed to researchers and graduate students in algebraic geometry, singularity theory, and algebraic topology. Most of the material in this volume has not yet appeared in book form.