Dimension Estimates for Hilbert Schemes and Effective Base Point Freeness on Moduli Spaces of Vector Bundles on Curves

نویسنده

  • MIHNEA POPA
چکیده

It is a well established fact that the solutions of many problems involving families of vector bundles should essentially depend on good estimates for the dimension of the Hilbert schemes of coherent quotients of a given bundle. Deformation theory provides basic cohomological dimension bounds, but most of the time the cohomology groups involved are hard to estimate accurately and moreover do not provide bounds that work uniformly. On smooth algebraic curves, an optimal answer to this problem has been previously given only in the case of quotients of minimal degree by Mukai and Sakai. If E is a vector bundle of rank r and

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Generalized Theta Linear Series on Moduli Spaces of Vector Bundles on Curves

Contents 1. Introduction 1 2. Semistable bundles 2 2.1. Arbitrary vector bundles 2 2.2. Semistable vector bundles 4 2.3. Example: Lazarsfeld's bundles 6 2.4. Example: Raynaud's bundles 8 2.5. The moduli space 9 3. Generalized theta divisors 11 4. Quot schemes and stable maps 14 5. Verlinde formula and Strange Duality 16 5.1. Verlinde formula 16 5.2. Strange Duality 18 6. Base points 20 6.1. Abs...

متن کامل

Fourier-mukai Transforms for Abelian Varieties and Moduli of Stable Bundles

We classify Fourier-Mukai transforms for abelian varieties. In the case of a principally polarized abelian surface these are then used to identify a large family of moduli spaces of stable vector bundles as Hilbert schemes of points on the surface.

متن کامل

Zero - dimensional Schemes on Abelian Surfaces

The moduli spaces of semistable torsion-free sheaves with c 1 = 0 and c 2 = ?2 and ?3 over a principally polarised complex torus are described explicitly in terms of zero-dimensional subschemes of the torus. The boundary structures are computed in detail. The rst moduli space is a compactiied family of Jacobians and the second is a Hilbert scheme. In this paper we shall show how detailed inform...

متن کامل

Universal moduli spaces of vector bundles and the log-minimal model program on the moduli of curves

Recent work on the log-minimal model program for the moduli space of curves, as well as past results of Caporaso, Pandharipande, and Simpson motivate an investigation of compactifications of the universal moduli space of slope semi-stable vector bundles over moduli spaces of curves arising in the Hassett–Keel program. Our main result is the construction of a universal moduli space of slope semi...

متن کامل

The Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves

We construct the Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves. The Hilbert compactification is the GIT quotient of some open part of an appropriate Hilbert scheme of curves in a Graßmannian. It has all the properties asked for by Teixidor.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2000