Variation of moduli spaces and Donaldson invariants under change of polarization

Abstract

The paper determines the change of moduli spaces of rank $2$ sheaves on surfaces with $p_g=0$ under change of polarization and the corresponding change of the Donaldson invariants. In this revised version we have made some minor stylistic changes in the previous text. In addition we have added a final chapter of about 20 pages (announced in the previous version), in which the six lowest order terms (three of them non-zero) of the change are computed explicitely using computations in the cohomology of Hilbert schemes of points.

44 pages, amslatex, no figures

References in corpus (1)

• Flips of moduli spaces and transition formulas for Donaldson polynomial invariants of rational surfaces

Cited by in corpus (5)

• Geometric constraints in dual F-theory and heterotic string compactifications
• Transitions in the Web of Heterotic Vacua
• Projectivity and Birational Geometry of Bridgeland moduli spaces
• Flips of moduli spaces and transition formulas for Donaldson polynomial invariants of rational surfaces
• Cosection localization and the Quot scheme ${\mathrm{Quot}}_S^l(\mathcal{E})$