Moduli spaces of 1-dimensional semi-stable sheaves and Strange duality on ${\mathbb{P}}^2$

Abstract

We study Le Potier's strange duality conjecture on ${\mathbb{P}}^2$. We show the conjecture is true for the pair ($W(2,0,2),M(d,0)$) with $d>0$, where $W(2,0,2)$ is the moduli space of semistable sheaves of rank 2, zero first Chern class and second Chern class 2, and $M(d,0)$ is the moduli space of 1-dimensional semistable sheaves of first Chern class $dH$ and Euler characteristic 0.

An appendix of 9 pages was added

References in corpus (2)

• The rank-level duality for non-abelian theta functions
• Generating functions for K-theoretic Donaldson invariants and Le Potier's strange duality