Toric Sheaves on Hirzebruch Orbifolds

2018/03/29 by Wang, Weikun
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.11215

Abstract

We provide a stacky fan description of the total space of certain split vector bundles, as well as their projectivization, over toric Deligne-Mumford stacks. We then specialize to the case of Hirzebruch orbifold H_r^ab obtained by projectivizing O ⊕ O(r) over the weighted projective line ℙ(a,b). Next, we give a combinatorial description of toric sheaves on H_r^ab and investigate their basic properties. With fixed choice of polarization and a generating sheaf, we describe the fixed point locus of the moduli scheme of μ-stable torsion free sheaves of rank 1 and 2 on H_r^ab. As an example, we obtain explicit formulas for generating functions of Euler characteristics of locally free sheaves of rank 2 on ℙ(1,2) × ℙ¹.

Related

• Fixed point loci of moduli spaces of sheaves on toric varieties
• Constructible sheaves on toric varieties
• Stable toric sheaves. I : Chern classes
• Existence of semistable sheaves on Hirzebruch surfaces
• Toric sheaves, stability and fibrations