Mumford-Thaddeus Principle on the Moduli Space of Vector Bundles on an Algebraic Surface

Details Mumford-Thaddeus Principle on the Moduli Space of Vector Bundles on an Algebraic Surface Mumford-Thaddeus Principle on the Moduli Space of Vector Bundles on an Algebraic Surface

1994-10-15

arxiv.org/abs/alg-geom/9410016v1

Mathematics

Algebraic Geometry

61 pages, amstex

Scientific paper

We study the behavior of the Gieseker space of semistable torsion-free sheaves of rank r and fixed c_1, c_2 on a non-singular projective surface as the polarization varies. It is shown that the ample cone admits a locally finite chamber structure, and that passing a wall adjacent to a pair of chambers has the effect of modifying the moduli space by a (finite) sequence of flips of the type studied by Thaddeus. The key steps are a modification of Simpson's method and the introduction of a "rationally twisted" moduli space. The result is more general but less explicit than the recent work of Ellingsrud-Goettsche (alg-geom/9410005) and Friedman-Qin (alg-geom/9410007).

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