Some Notes on the Moduli of Stable Sheaves on Elliptic Surfaces
نویسندگان
چکیده
In this paper, we shall consider the birational structure of moduli of stable sheaves on elliptic surfaces, which is a generalization of Friedman’s results to higher rank cases. As applications, we show that some moduli spaces of stable sheaves on P 2 are rational. We also compute the Picard groups of those on Abelian surfaces.
منابع مشابه
Stable Rank-2 Bundles on Calabi-yau Manifolds
Recently there is a surge of research interest in the construction of stable vector bundles on Calabi-Yau manifolds motivated by questions from string theory. An interesting aspect of the moduli spaces of stable sheaves on Calabi-Yau manifolds is their relation to the higher dimensional gauge theory studied by Donaldson, R. Thomas and Tian et al. [D-T, Tho, Tia]. A holomorphic Casson invariant ...
متن کاملStructure of the Moduli Space of Stable Sheaves on Elliptic Fibrations D. Hern Andez Ruip Erez
We describe a method for characterizing certain connected components of the moduli space M(a; b) of torsion-free sheaves on a elliptic surface X with a section which are stable with respect to a polarization of type aH + bb, H being the section and the elliptic bre (b 0) and whose relative degree is zero. We construct all sheaves in these components as Fourier-Mukai transforms of the pure dimen...
متن کاملSemi-homogeneous Sheaves, Fourier-mukai Transforms and Moduli of Stable Sheaves on Abelian Surfaces
This paper studies stable sheaves on abelian surfaces of Picard number one. Our main tools are semi-homogeneous sheaves and Fourier-Mukai transforms. We introduce the notion of semi-homogeneous presentation and investigate the behavior of stable sheaves under Fourier-Mukai transforms. As a consequence, an affirmative proof is given to the conjecture proposed by Mukai in the 1980s. This paper al...
متن کاملLectures on Moduli Spaces of Elliptic Curves
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. 1 Their goal is to introduce and motivate basic concepts and constructions important in the study of moduli spaces of curves and abelian varieties through the example of elliptic curves. The advantage of working with elliptic curves is that most constructio...
متن کاملDesingularization of Some Moduli Scheme of Stable Sheaves on a Surface
Let X be a nonsingular projective surface over an algebraically closed field with characteristic 0, and H − and H+ ample line bundles on X separated by only one wall of type (c1, c2). Suppose the moduli scheme M(H−) of rank-two H − -stable sheaves with Chern classes (c1, c2) is non-singular. We shall construct a desingularization of M(H+) by using M(H−). As an application, we consider whether s...
متن کاملذخیره 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 1999