Donaldson type invariants for algebraic surfaces: transition of moduli stacks

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 conjectur”" 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! INDICE: 1. Introduction.- 2. Preliminaries.- 3. Parabolic L-Bradlow pairs.- 4. Geometric Invariant Theory and Enhanced Master Space.- 5. Obstruction Theories of Moduli Stacks and Master Spaces.- 6. Virtual Fundamental Classes.- 7.Invariants.

• ISBN: 978-3-540-93912-2
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 410
• Fecha Publicación: 01/03/2009
• Nº Volúmenes: 1
• Idioma: Inglés