16 6 Configurations And Geometry Of Kummer Surfaces In

Author : Maria del Rosario Gonzalez-Dorrego
Publisher : American Mathematical Society(RI)
Page : 114 pages
File Size : 47,8 Mb
Release : 2014-08-31
Category : MATHEMATICS
ISBN : 1470400898

Get Book

16,6 Configurations and Geometry of Kummer Surfaces in by Maria del Rosario Gonzalez-Dorrego Pdf

This monograph studies the geometry of a Summer surface in P ]3 and of its minimal desingularization, which is a K3 surface (here k is an algebraically closed field of characteristic different from 2). This Kummer surface is a quartic surface with sixteen nodes as its only singularities. These nodes give rise to a configuration of sixteen points and sixteen planes in P ]3 such that each plane contains exactly six points and each point belongs to exactly six planes (this is called a (16, 6) configuration). A Kummer surface is uniquely determined by its set of nodes. Gonzalez_Dorrego classifies (16, 6) configurations and studies their manifold symmetries and the underlying questions about finite subgroups of PGL [4 ( k ). She uses this information to give a complete classification of Kummer surfaces with explicit equations and explicit descriptions of their singularities. In addition, the beautiful connections to the theory of K3 surfaces and abelian varieties are studied.

Author : Maria del Rosario Gonzalez-Dorrego
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 54,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825747

Get Book

$(16,6)$ Configurations and Geometry of Kummer Surfaces in ${\mathbb P}^3$ by Maria del Rosario Gonzalez-Dorrego Pdf

The philosophy of the first part of this work is to understand (and classify) Kummer surfaces by studying (16, 6) configurations. Chapter 1 is devoted to classifying (16, 6) configurations and studying their manifold symmetries and the underlying questions about finite subgroups of [italic capitals]PGL4([italic]k). In chapter 2 we use this information to give a complete classification of Kummer surfaces together with explicit equations and the explicit description of their singularities.

Author : Thomas Dedieu,Flaminio Flamini,Claudio Fontanari,Concettina Galati,Rita Pardini
Publisher : Springer Nature
Page : 421 pages
File Size : 47,5 Mb
Release : 2023-04-14
Category : Mathematics
ISBN : 9783031119385

Get Book

The Art of Doing Algebraic Geometry by Thomas Dedieu,Flaminio Flamini,Claudio Fontanari,Concettina Galati,Rita Pardini Pdf

This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.

Author : Ron Donagi,Tony Shaska
Publisher : Cambridge University Press
Page : 537 pages
File Size : 49,9 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9781108715775

Get Book

Integrable Systems and Algebraic Geometry by Ron Donagi,Tony Shaska Pdf

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Author : Antonio Campillo Lopez,Luis Narvaez Macarro
Publisher : Birkhäuser
Page : 418 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890205

Get Book

Algebraic Geometry and Singularities by Antonio Campillo Lopez,Luis Narvaez Macarro Pdf

The focus of this volume lies on singularity theory in algebraic geometry. It includes papers documenting recent and original developments and methods in subjects such as resolution of singularities, D-module theory, singularities of maps and geometry of curves. The papers originate from the Third International Conference on Algebraic Geometry held in La Rbida, Spain, in December 1991. Since then, the articles have undergone a meticulous process of refereeing and improvement, and they have been organized into a comprehensive account of the state of the art in this field.

Author : Anne Frühbis-Krüger,Remke Nanne Kloosterman,Matthias Schütt
Publisher : Springer
Page : 324 pages
File Size : 52,9 Mb
Release : 2014-10-01
Category : Mathematics
ISBN : 9783319054049

Get Book

Algebraic and Complex Geometry by Anne Frühbis-Krüger,Remke Nanne Kloosterman,Matthias Schütt Pdf

Several important aspects of moduli spaces and irreducible holomorphic symplectic manifolds were highlighted at the conference “Algebraic and Complex Geometry” held September 2012 in Hannover, Germany. These two subjects of recent ongoing progress belong to the most spectacular developments in Algebraic and Complex Geometry. Irreducible symplectic manifolds are of interest to algebraic and differential geometers alike, behaving similar to K3 surfaces and abelian varieties in certain ways, but being by far less well-understood. Moduli spaces, on the other hand, have been a rich source of open questions and discoveries for decades and still continue to be a hot topic in itself as well as with its interplay with neighbouring fields such as arithmetic geometry and string theory. Beyond the above focal topics this volume reflects the broad diversity of lectures at the conference and comprises 11 papers on current research from different areas of algebraic and complex geometry sorted in alphabetic order by the first author. It also includes a full list of speakers with all titles and abstracts.

Author : Viktoria Heu,Frank Loray
Publisher : American Mathematical Soc.
Page : 103 pages
File Size : 51,8 Mb
Release : 2019-06-10
Category : Electronic
ISBN : 9781470435660

Get Book

Flat Rank Two Vector Bundles on Genus Two Curves by Viktoria Heu,Frank Loray Pdf

The authors study the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which they compute a natural Lagrangian rational section. As a particularity of the genus case, connections as above are invariant under the hyperelliptic involution: they descend as rank logarithmic connections over the Riemann sphere. The authors establish explicit links between the well-known moduli space of the underlying parabolic bundles with the classical approaches by Narasimhan-Ramanan, Tyurin and Bertram. This allows the authors to explain a certain number of geometric phenomena in the considered moduli spaces such as the classical -configuration of the Kummer surface. The authors also recover a Poincaré family due to Bolognesi on a degree 2 cover of the Narasimhan-Ramanan moduli space. They explicitly compute the Hitchin integrable system on the moduli space of Higgs bundles and compare the Hitchin Hamiltonians with those found by van Geemen-Previato. They explicitly describe the isomonodromic foliation in the moduli space of vector bundles with -connection over curves of genus 2 and prove the transversality of the induced flow with the locus of unstable bundles.

Author : Daniel Huybrechts
Publisher : Cambridge University Press
Page : 499 pages
File Size : 54,7 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9781107153042

Get Book

Lectures on K3 Surfaces by Daniel Huybrechts Pdf

Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

Author : Gianfranco Casnati,Alberto Conte,Letterio Gatto,Livia Giacardi,Marina Marchisio,Alessandro Verra
Publisher : Birkhäuser
Page : 756 pages
File Size : 54,9 Mb
Release : 2017-04-20
Category : Mathematics
ISBN : 9783319329949

Get Book

From Classical to Modern Algebraic Geometry by Gianfranco Casnati,Alberto Conte,Letterio Gatto,Livia Giacardi,Marina Marchisio,Alessandro Verra Pdf

This book commemorates the 150th birthday of Corrado Segre, one of the founders of the Italian School of Algebraic Geometry and a crucial figure in the history of Algebraic Geometry. It is the outcome of a conference held in Turin, Italy. One of the book's most unique features is the inclusion of a previously unpublished manuscript by Corrado Segre, together with a scientific commentary. Representing a prelude to Segre's seminal 1894 contribution on the theory of algebraic curves, this manuscript and other important archival sources included in the essays shed new light on the eminent role he played at the international level. Including both survey articles and original research papers, the book is divided into three parts: section one focuses on the implications of Segre's work in a historic light, while section two presents new results in his field, namely Algebraic Geometry. The third part features Segre's unpublished notebook: Sulla Geometria Sugli Enti Algebrici Semplicemente Infiniti (1890-1891). This volume will appeal to scholars in the History of Mathematics, as well as to researchers in the current subfields of Algebraic Geometry.

Author : Carlos Andradas,Jesús M. Ruiz
Publisher : American Mathematical Soc.
Page : 117 pages
File Size : 50,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821826126

Get Book

Algebraic and Analytic Geometry of Fans by Carlos Andradas,Jesús M. Ruiz Pdf

A set which can be defined by systems of polynomial inequalities is called semialgebraic. When such a description is possible locally around every point, by means of analytic inequalities varying with the point, the set is called semianalytic. If one single system of strict inequalities is enough, either globally or locally at every point, the set is called basic. The topic of this work is the relationship between these two notions. Namely, Andradas and Ruiz describe and characterize, both algebraically and geometrically, the obstructions for a basic semianalytic set to be basic semialgebraic. Then they describe a special family of obstructions that suffices to recognize whether or not a basic semianalytic set is basic semialgebraic. Finally, they use the preceding results to discuss the effect on basicness of birational transformations.

Author : Chandrashekar Adiga
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 47,5 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821823163

Get Book

Chapter 16 of Ramanujan's Second Notebook: Theta-Functions and $q$-Series by Chandrashekar Adiga Pdf

Author : Maria del Rosario Gonzalez-Dorrego
Publisher : Unknown
Page : 248 pages
File Size : 47,9 Mb
Release : 1990
Category : Dissertations, Academic
ISBN : UCAL:C3364929

Get Book

Curves on Kummer Surfaces in P3 by Maria del Rosario Gonzalez-Dorrego Pdf

Author : David Chudnovsky,Gregory Chudnovsky,Melvyn B. Nathanson
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 51,6 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9781441990600

Get Book

Number Theory by David Chudnovsky,Gregory Chudnovsky,Melvyn B. Nathanson Pdf

This volume of new research papers marks the 20th anniversary of the New York Number Theory Seminar (NYNTS). Since 1982, NYNTS has presented a range of research in number theory and related fields of mathematics, from physics to geometry to combinatorics and computer science. The speakers have included Field medalists as well as promising lesser known mathematicians whose theorems are significant. The papers presented here are all previously unpublished.

Author : S. Coen
Publisher : Routledge
Page : 520 pages
File Size : 54,7 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351445283

Get Book

Geometry and Complex Variables by S. Coen Pdf

This reference presents the proceedings of an international meeting on the occasion of theUniversity of Bologna's ninth centennial-highlighting the latest developments in the field ofgeometry and complex variables and new results in the areas of algebraic geometry,differential geometry, and analytic functions of one or several complex variables.Building upon the rich tradition of the University of Bologna's great mathematics teachers, thisvolume contains new studies on the history of mathematics, including the algebraic geometrywork of F. Enriques, B. Levi, and B. Segre ... complex function theory ideas of L. Fantappie,B. Levi, S. Pincherle, and G. Vitali ... series theory and logarithm theory contributions of P.Mengoli and S. Pincherle ... and much more. Additionally, the book lists all the University ofBologna's mathematics professors-from 1860 to 1940-with precise indications of eachcourse year by year.Including survey papers on combinatorics, complex analysis, and complex algebraic geometryinspired by Bologna's mathematicians and current advances, Geometry and ComplexVariables illustrates the classic works and ideas in the field and their influence on today'sresearch.

Author : Jaume Llibre,Ana Nunes
Publisher : American Mathematical Soc.
Page : 191 pages
File Size : 49,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825815

Get Book

Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations by Jaume Llibre,Ana Nunes Pdf

This work presents a study of the foliations of the energy levels of a class of integrable Hamiltonian systems by the sets of constant energy and angular momentum. This includes a classification of the topological bifurcations and a dynamical characterization of the critical leaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonian perturbations of this class of integrable Hamiltonians and give conditions for the persistence of the separatrix structure of the foliations and for the existence of transversal ejection-collision orbits of the perturbed system. Finally, they consider a class of non-Hamiltonian perturbations of a family of integrable systems of the type studied earlier and prove the persistence of 'almost all' the tori and cylinders that foliate the energy levels of the unperturbed system as a consequence of KAM theory.