Estimates of sections of determinant line bundles on Moduli spaces of pure sheaves on algebraic surfaces

Abstract

Let $X$ be any smooth simply connected projective surface. We consider some moduli space of pure sheaves of dimension one on $X$, i.e. $\mhu$ with $u=(0,L,\chi (u)=0)$ and $L$ an effective line bundle on $X$, together with a series of determinant line bundles associated to $r[\mo_X]-n[\mo_{pt}]$ in Grothendieck group of $X$. Let $g_L$ denote the arithmetic genus of curves in the linear system $\ls$. For $g_L\le 2$, we give a upper bound of the dimensions of sections of these line bundles by restricting them to a generic projective line in $\ls$. Our result gives, together with Göttsche's computation, a first step of a check for the strange duality for some cases for $X$ a rational surface.

References in corpus (2)

• On the Cobordism Class of the Hilbert Scheme of a Surface
• A functorial construction of moduli of sheaves