Finiteness of isomorphic classes in the set of moduli schemes of sheaves on a surface

Details Finiteness of isomorphic classes in the set of moduli schemes of sheaves on a surface Finiteness of isomorphic classes in the set of moduli schemes of sheaves on a surface

2010-01-15

arxiv.org/abs/1001.2629v1

Mathematics

Algebraic Geometry

Scientific paper

When a non-singular complex projective surface $X$ satisfies that $K_X\sim
0$, we shall show that there are only finitely many isomorphic classes as
abstract schemes in the set of moduli scheme of $H$-semistable sheaves with
fixed Chern classes $\alpha$ on $X$, where $H$ runs over the set of all
$\alpha$-generic polarizations on $X$.

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