Strange duality on rational surfaces

2016/04/19 by Yuan, Yao
#14D05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.05509

Abstract

We study Le Potier's strange duality conjecture on a rational surface. We focus on the case involving the moduli space of rank 2 sheaves with trivial first Chern class and second Chern class 2, and the moduli space of 1-dimensional sheaves with determinant L and Euler characteristic 0. We show the conjecture for this case is true under some suitable conditions on L, which applies to L ample on any Hirzebruch surface Σ_e:=ℙ(O_ℙ¹\oplusO_ℙ¹(e)) except for e=1. When e=1, our result applies to L=aG+bF with b≥ a+[a/2], where F is the fiber class, G is the section class with G²=-1 and [a/2] is the integral part of a/2.

Related

• Strange duality on rational surfaces II: higher rank cases
• Moduli spaces of 1-dimensional semi-stable sheaves and Strange duality on ℙ²
• On the strange duality conjecture for abelian surfaces
• On the strange duality conjecture for abelian surfaces II
• Sheaves on abelian surfaces and Strange Duality