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Stable pairs on local K3 surfaces.

Date: 
Tuesday 12th April 2011 - 10:00 to 11:00
Venue: 
INI Seminar Room 1
Abstract: 
I give a formula which relates Euler characteristic of moduli spaces of stable pairs on local K3 surfaces to counting invariants of semistable sheaves on them. The formula generalizes Kawai-Yoshioka's formula for stable pairs with irreducible curve classes to arbitrary curve classes. I also propose a conjectual multi-covering formula of sheaf counting invariants which, combined with the main result, leads to an Euler characteristic version of Katz-Klemm-Vafa conjecture for stable pairs.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons