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Donaldson Type Invariants for Algebraic Surfaces [electronic resource] : Transition of Moduli Stacks / by Takuro Mochizuki.

Por: Mochizuki, Takuro [author.]Tipo de material: TextoTextoSeries Lecture Notes in Mathematics, 1972Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Descripción: online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783540939139Trabajos contenidos: SpringerLink (Online service)Tema(s): Mathematics | Geometry, algebraic | Mathematics | Algebraic GeometryFormatos físicos adicionales: Sin títuloRecursos en línea: de clik aquí para ver el libro electrónico
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Springer eBooksResumen: We are defining and studying an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface.We are interested in relations among the invariants, which are natural generalizations of the "wall-crossing formula" and the "Witten conjecture" for classical Donaldson invariants. Our goal is to obtain a weaker version of these relations, by systematically using the intrinsic smoothness of moduli spaces. According to the recent excellent work of L. Goettsche, H. Nakajima and K. Yoshioka, the wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case!
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Preliminaries -- Parabolic L-Bradlow Pairs -- Geometric Invariant Theory and Enhanced Master Space -- Obstruction Theories of Moduli Stacks and Master Spaces -- Virtual Fundamental Classes -- Invariants.

We are defining and studying an algebro-geometric analogue of Donaldson invariants by using moduli spaces of semistable sheaves with arbitrary ranks on a polarized projective surface.We are interested in relations among the invariants, which are natural generalizations of the "wall-crossing formula" and the "Witten conjecture" for classical Donaldson invariants. Our goal is to obtain a weaker version of these relations, by systematically using the intrinsic smoothness of moduli spaces. According to the recent excellent work of L. Goettsche, H. Nakajima and K. Yoshioka, the wall-crossing formula for Donaldson invariants of projective surfaces can be deduced from such a weaker result in the rank two case!

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