Strange duality on P2 via quiver representations

We study Le Potier's strange duality conjecture on P2. We focus on the strange duality map SDc,d which involves the moduli space of rank r sheaves with trivial first Chern class and second Chern class n, and the moduli space of 1-dimensional sheaves with determinant O-P2 (d) and Euler characteristic 0. By using tools in quiver representation theory, we show that SDc,d is an isomorphism for r = n or r = n - 1 or d <= 3, and in general SDc,dn is injective for any n >= r > 0 and d > 0. (C) 2020 Elsevier Inc. All rights reserved.