Titlebook: Donaldson Type Invariants for Algebraic Surfaces; Transition of Moduli Takuro Mochizuki Book 2009 Springer-Verlag Berlin Heidelberg 2009 Ex

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Introduction,, transition formulas are stated under an assumption which makes the problems much simpler. They are enough for the study of invariants in the rank 2 case, and the results are explained in Section 1.4. Generalization to the higher rank case is discussed in Section 1.5. We explain how to use master spaces for our problems in Section 1.6.

radiograph

COMA

Preliminaries,on 2.4.3. It gives obstruction theories of moduli spaces of torsion-free quotient sheaves over a smooth projective surface. The result will be used in Section 5.6. We also obtain the smoothness of moduli spaces of quotient torsion-sheaves over a smooth projective curve, although we will not use it l

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Geometric Invariant Theory and Enhanced Master Space,n Section 4.5, we construct an enhanced master space in the oriented case, and we give a description of the stack theoretic fixed point set with respect to the natural torus action. They are essentially just a reformulation of the results in the previous sections.We give a more convenient descriptio

Infinitesimal

Obstruction Theories of Moduli Stacks and Master Spaces, construction of obstruction theories of master spaces. In Subsection 5.1.4, we give an obstruction theory of the open subset of a moduli stack of torsion-free sheaves determined by the condition O., by directly applying the construction in Subsection 5.1.1. As a special case, we look at an obstruct

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Unerwartete Todesf?lle in Klinik und Praxison 2.4.3. It gives obstruction theories of moduli spaces of torsion-free quotient sheaves over a smooth projective surface. The result will be used in Section 5.6. We also obtain the smoothness of moduli spaces of quotient torsion-sheaves over a smooth projective curve, although we will not use it l

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