This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces. The first part introduces the basic concepts in the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration, Grothendieck's Quot-scheme. It presents detailed proofs of the Grauert-MA¼lich Theorem, the Bogomolov Inequality, the semistability of tensor products, and the boundedness of the family of semistable sheaves. It also gives a self-contained account of the construction of moduli spaces of semistable sheaves on a projective variety An la Gieseker, Maruyama, and Simpson. The second part presents some of the recent results of the geometry of moduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to curves, symplectic structures, irreducibility and Kodaira-dimension of moduli spaces.This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces.

Title | : | The Geometry of Moduli Spaces of Sheaves |

Author | : | Daniel Huybrechts, Manfred Lehn |

Publisher | : | Vieweg+Teubner Verlag - 2013-11-13 |

You must register with us as either a Registered User before you can Download this Book. You'll be greeted by a simple sign-up page.

Once you have finished the sign-up process, you will be redirected to your download Book page.

`1.`Register a free 1 month Trial Account.`2.`Download as many books as you like (Personal use)`3.`Cancel the membership at any time if not satisfied.