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Author : Manfred Lehn
Release : 1997
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Chern Classes of Tautological Sheaves on Hilbert Schemes of Points on Surfaces by : Manfred Lehn
Download or read book Chern Classes of Tautological Sheaves on Hilbert Schemes of Points on Surfaces written by Manfred Lehn. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andreas Krug
Release : 2012
Genre : Mathematics
Kind : eBook
Book Rating : 544/5 ( reviews)
Book Synopsis Extension Groups of Tautological Sheaves on Hilbert Schemes of Points on Surfaces by : Andreas Krug
Download or read book Extension Groups of Tautological Sheaves on Hilbert Schemes of Points on Surfaces written by Andreas Krug. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Hiraku Nakajima
Release : 1999
Genre : Mathematics
Kind : eBook
Book Rating : 569/5 ( reviews)
Book Synopsis Lectures on Hilbert Schemes of Points on Surfaces by : Hiraku Nakajima
Download or read book Lectures on Hilbert Schemes of Points on Surfaces written by Hiraku Nakajima. This book was released on 1999. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Takuro Mochizuki
Release : 2009-04-20
Genre : Mathematics
Kind : eBook
Book Rating : 13X/5 ( reviews)
Book Synopsis Donaldson Type Invariants for Algebraic Surfaces by : Takuro Mochizuki
Download or read book Donaldson Type Invariants for Algebraic Surfaces written by Takuro Mochizuki. This book was released on 2009-04-20. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, we de?ne and investigate an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. We may expect the existence of interesting “universal relations among invariants”, which would be a natural generalization of the “wall-crossing formula” and the “Witten conjecture” for classical Donaldson invariants. Our goal is to obtain a weaker version of such relations, in other brief words, to describe a relation as the sum of integrals over the products of m- uli spaces of objects with lower ranks. Fortunately, according to a recent excellent work of L. Gottsche, ̈ H. Nakajima and K. Yoshioka, [53], a wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case. We hope that our work in this monograph would, at least tentatively, provides a part of foundation for the further study on such universal relations. In the rest of this preface, we would like to explain our motivation and some of important ingredients of this study. See Introduction for our actual problems and results. Donaldson Invariants Let us brie?y recall Donaldson invariants. We refer to [22] for more details and precise. We also refer to [37], [39], [51] and [53]. LetX be a compact simply con- ? nected oriented real 4-dimensional C -manifold with a Riemannian metric g. Let P be a principalSO(3)-bundle on X.
Author : Zhenbo Qin
Release : 2018-02-26
Genre : Mathematics
Kind : eBook
Book Rating : 888/5 ( reviews)
Book Synopsis Hilbert Schemes of Points and Infinite Dimensional Lie Algebras by : Zhenbo Qin
Download or read book Hilbert Schemes of Points and Infinite Dimensional Lie Algebras written by Zhenbo Qin. This book was released on 2018-02-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.
