Donaldson type invariants for algebraic surfaces : transition of moduli stacks / Takuro Mochizuki

Auteur principal : Mochizuki, Takuro, 1972-, AuteurType de document : Livre numériqueCollection : Lecture notes in mathematics, 1972Langue : anglais.Éditeur : Berlin : Springer, 2009ISBN: 9783540939122.ISSN: 1617-9692.Sujet MSC : 14D20, Families, fibrations in algebraic geometry, Algebraic moduli problems, moduli of vector bundles
14-02, Research exposition (monographs, survey articles) pertaining to algebraic geometry
14J80, Algebraic geometry - Surfaces and higher-dimensional varieties, Topology of surfacesEn-ligne : Springerlink | Zentralblatt
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In this book, the author defines and studies an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface. The existence of interesting universal relations among these invariants, which would be natural generalizations of the wall-crossing formula and the Witten conjecture for the classical Donaldson invariants, is expected. The goal is to obtain a weaker version of such relations, i.e., to obtain a relation as the sum of integrals over the products of moduli spaces of objects with lower ranks. ... (Zentralblatt)

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