Hyperkahler Manifolds Hyperholomorphic Sheaves And New Examples Of Hyperk Hler Manifolds

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Hyperkahler Manifolds Hyperholomorphic Sheaves And New Examples Of Hyperk Hler Manifolds

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Author : Misha Verbitsky
language : en
Publisher: American Mathematical Society(RI)
Release Date : 1999

Hyperkahler Manifolds Hyperholomorphic Sheaves And New Examples Of Hyperk Hler Manifolds written by Misha Verbitsky and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

This volume introduces hyperkahler manifolds to those who have not previously studied them. The book is divided into two parts on: hyperholomorphic sheaves and examples of hyperkahler manifolds; and hyperkahler structures on total spaces of holomorphic cotangent bundles.

Hodge Cycles Motives And Shimura Varieties

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Author : Pierre Deligne
language : en
Publisher: Springer Science & Business Media
Release Date : 1982

Hodge Cycles Motives And Shimura Varieties written by Pierre Deligne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.

This volume collects six related articles. The first is the notes (written by J.S. Milne) of a major part of the seminar "Periodes des Int grales Abeliennes" given by P. Deligne at I'.B.E.S., 1978-79. The second article was written for this volume (by P. Deligne and J.S. Milne) and is largely based on: N Saavedra Rivano, Categories tannakiennes, Lecture Notes in Math. 265, Springer, Heidelberg 1972. The third article is a slight expansion of part of: J.S. Milne and Kuang-yen Shih, Sh ura varieties: conjugates and the action of complex conjugation 154 pp. (Unpublished manuscript, October 1979). The fourth article is based on a letter from P. De1igne to R. Langlands, dated 10th April, 1979, and was revised and completed (by De1igne) in July, 1981. The fifth article is a slight revision of another section of the manuscript of Milne and Shih referred to above. The sixth article, by A. Ogus, dates from July, 1980.

Hyperholomorphic Sheaves And New Examples Of Hyperk Hler Manifolds

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Author : Misha Verbitsky
language : en
Publisher:
Release Date : 1998

Hyperholomorphic Sheaves And New Examples Of Hyperk Hler Manifolds written by Misha Verbitsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Chern Numbers And Rozansky Witten Invariants Of Compact Hyper K Hler Manifolds

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Author : Marc Nieper-Wisskirchen
language : en
Publisher: World Scientific
Release Date : 2004

Chern Numbers And Rozansky Witten Invariants Of Compact Hyper K Hler Manifolds written by Marc Nieper-Wisskirchen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This unique book deals with the theory of Rozansky?Witten invariants, introduced by L Rozansky and E Witten in 1997. It covers the latest developments in an area where research is still very active and promising. With a chapter on compact hyper-K„hler manifolds, the book includes a detailed discussion on the applications of the general theory to the two main example series of compact hyper-K„hler manifolds: the Hilbert schemes of points on a K3 surface and the generalized Kummer varieties.

Toeplitz Operators On K Hler Manifolds

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Author : Tatyana Barron
language : en
Publisher: Springer
Release Date : 2018-07-24

Toeplitz Operators On K Hler Manifolds written by Tatyana Barron and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-24 with Mathematics categories.

The purpose of this Brief is to give a quick practical introduction into the subject of Toeplitz operators on Kähler manifolds, via examples, worked out carefully and in detail. Necessary background is included. Several theorems on asymptotics of Toeplitz operators are reviewed and illustrated by examples, including the case of tori and the 2-dimensional sphere. Applications in the context of multisymplectic and hyperkähler geometry are discussed. The book is suitable for graduate students, advanced undergraduate students, and any researchers.

On Birational Transformations And Automorphisms Of Some Hyperk Hler Manifolds

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Author : Pietro Beri
language : en
Publisher:
Release Date : 2020

On Birational Transformations And Automorphisms Of Some Hyperk Hler Manifolds written by Pietro Beri and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.

My thesis work focuses on double EPW sextics, a family of hyperkähler manifolds which, in the general case, are equivalent by deformation to Hilbert's scheme of two points on a K3 surface. In particular I used the link that these manifolds have with Gushel-Mukai varieties, which are Fano varieties in a Grassmannian if their dimension is greater than two, K3 surfaces if their dimension is two.The first chapter contains some reminders of the theory of Pell's equations and lattices, which are fundamental for the study of hyperkähler manifolds. Then I recall the construction which associates a double covering to a sheaf on a normal variety.In the second chapter I discuss hyperkähler manifolds and describe their first properties; I also introduce the first case of hyperkähler manifold that has been studied, the K3 surfaces. This family of surfaces corresponds to the hyperkähler manifolds in dimension two.Furthermore, I briefly present some of the latest results in this field, in particular I define different module spaces of hyperkähler manifolds, and I describe the action of automorphism on the second cohomology group of a hyperkähler manifold.The tools introduced in the previous chapter do not provide a geometrical description of the action of automorphism on the manifold for the case of the Hilbert scheme of points on a general K3 surface. In the third chapter, I therefore introduce a geometrical description up to a certain deformation. This deformation takes into account the structure of Hilbert scheme. To do so, I introduce an isomorphism between a connected component of the module space of manifolds of type K3[n] with a polarization, and the module space of manifolds of the same type with an involution of which the rank of the invariant is one. This is a generalization of a result obtained by Boissière, An. Cattaneo, Markushevich and Sarti in dimension two. The first two parts of this chapter are a joint work with Alberto Cattaneo.In the fourth chapter, I define EPW sextics, using O'Grady's argument, which shows that a double covering of a EPW sextic in the general case is deformation equivalent to the Hilbert square of a K3 surface. Next, I present the Gushel-Mukai varieties, with emphasis on their connection with EPW sextics; this approach was introduced by O'Grady, continued by Iliev and Manivel and systematized by Kuznetsov and Debarre.In the fifth chapter, I use the tools introduced in the fourth chapter in the case where a K3 surface can be associated to a EPW sextic X. In this case I give explicit conditions on the Picard group of the surface for X to be a hyperkähler manifold. This allows to use Torelli's theorem for a K3 surface to demonstrate the existence of some automorphisms on X. I give some bounds on the structure of a subgroup of automorphisms of a sextic EPW under conditions of existence of a fixed point for the action of the group.Still in the case of the existence of a K3 surface associated with a EPW sextic X, I improve the bound obtained previously on the automorphisms of X, by giving an explicit link with the number of conics on the K3 surface. I show that the symplecticity of an automorphism on X depends on the symplecticity of a corresponding automorphism on the surface K3.The sixth chapter is a work in collaboration with Alberto Cattaneo. I study the group of birational automorphisms on Hilbert's scheme of points on a projective surface K3, in the generic case. This generalizes the result obtained in dimension two by Debarre and Macrì. Then I study the cases where there is a birational model where these automorphisms are regular. I describe in a geometrical way some involutions, whose existence has been proved before.