Lectures On Hilbert Schemes Of Points On Surfaces PDF Download
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Author | : Hiraku Nakajima |
Publisher | : American Mathematical Soc. |
Total Pages | : 146 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 0821819569 |
Download Lectures on Hilbert Schemes of Points on Surfaces Book in PDF, ePub and Kindle
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 | : Daniel Huybrechts |
Publisher | : Cambridge University Press |
Total Pages | : 499 |
Release | : 2016-09-26 |
Genre | : Mathematics |
ISBN | : 1316797252 |
Download Lectures on K3 Surfaces Book in PDF, ePub and Kindle
K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
Author | : Jacques Hurtubise and Eyal Markman |
Publisher | : American Mathematical Soc. |
Total Pages | : 268 |
Release | : |
Genre | : Algebra, Abstract |
ISBN | : 9780821870334 |
Download Algebraic Structures and Moduli Spaces Book in PDF, ePub and Kindle
This book contains recent and exciting developments on the structure of moduli spaces, with an emphasis on the algebraic structures that underlie this structure. Topics covered include Hilbert schemes of points, moduli of instantons, coherent sheaves and their derived categories, moduli of flat connections, Hodge structures, and the topology of affine varieties. Two beautiful series of lectures are a particularly fine feature of the book. One is an introductory series by Manfred Lehn on the topology and geometry of Hilbert schemes of points on surfaces, and the other, by Hiraku Nakajima and Kota Yoshioka, explains their recent work on the moduli space of instantons over ${\mathbb R 4$. The material is suitable for graduate students and researchers interested in moduli spaces in algebraic geometry, topology, and mathematical physics.
Author | : Zhenbo Qin |
Publisher | : American Mathematical Soc. |
Total Pages | : 336 |
Release | : 2018-02-26 |
Genre | : Hilbert schemes |
ISBN | : 1470441888 |
Download Hilbert Schemes of Points and Infinite Dimensional Lie Algebras Book in PDF, ePub and Kindle
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 | : Daniel Huybrechts |
Publisher | : Cambridge University Press |
Total Pages | : 345 |
Release | : 2010-05-27 |
Genre | : Mathematics |
ISBN | : 1139485822 |
Download The Geometry of Moduli Spaces of Sheaves Book in PDF, ePub and Kindle
This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.
Author | : Andreas Krug |
Publisher | : Logos Verlag Berlin GmbH |
Total Pages | : 130 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 3832532544 |
Download Extension Groups of Tautological Sheaves on Hilbert Schemes of Points on Surfaces Book in PDF, ePub and Kindle
In this thesis cohomological invariants of tensor products of tautological objects in the derived category of Hilbert schemes of points on surfaces are studied. The main tool is the Bridgeland-King-Reid-Haiman equivalence between the derived category of the Hilbert scheme and the equivariant derived category of the cartesian power of the surface. The work of Scala on this topic is further developed leading to a new description of the image of tensor products of tautological bundles under the BKRH equivalence. This description leads to formulas for the Euler characteristics of triple tensor products of tautological objects for arbitrary n and for arbitrary tensor products in the case n=2. Furthermore a formula for the extension groups between tautological objects is proven and the Yoneda product is described.
Author | : Anthony Ayers Iarrobino |
Publisher | : American Mathematical Soc. |
Total Pages | : 124 |
Release | : 1977 |
Genre | : Mathematics |
ISBN | : 0821821881 |
Download Punctual Hilbert Schemes Book in PDF, ePub and Kindle
This paper is about the structure of families of open ideals in the ring [italic]R of power series in two variables. The Hilbert scheme Hilb[italic superscript]n [italic]R parametrizing them is stratified into locally closed subschemes [italic]Z[italic subscript]T, whose dimensions we calculate.
Author | : Barbara Fantechi |
Publisher | : American Mathematical Soc. |
Total Pages | : 354 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 0821842455 |
Download Fundamental Algebraic Geometry Book in PDF, ePub and Kindle
Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.
Author | : Maurizio Cornalba |
Publisher | : World Scientific |
Total Pages | : 716 |
Release | : 1989-06-01 |
Genre | : Mathematics |
ISBN | : 9814590878 |
Download Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces Book in PDF, ePub and Kindle
Author | : Zhenbo Qin |
Publisher | : |
Total Pages | : |
Release | : 2018 |
Genre | : MATHEMATICS |
ISBN | : 9781470443894 |
Download Hilbert Schemes of Points and Infinite Dimensional Lie Algebras Book in PDF, ePub and Kindle