Strange duality on ℙ² via quiver representations

2018/07/24 by Yuan, Yao
#14D05 #14D22 #14J26 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.09172

Abstract

We study Le Potier's strange duality conjecture on ℙ². We focus on the strange duality map SD_cn^r,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 SD_c^rn,d is an isomorphisms for r=n or r=n-1 or d≤ 3, and in general SD_c^rn,d is injective for any n≥ r>0 and d>0.

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