Toric Sheaves on Hirzebruch Orbifolds
Weikun WangDepartment of Mathematics, University of Maryland, College Park, MD 20742, USA
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 obtained by projectivizing over the weighted projective line . Next, we give a combinatorial description of toric sheaves on 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 -stable torsion free sheaves of rank and on . As an example, we obtain explicit formulas for generating functions of Euler characteristics of locally free sheaves of rank 2 on .
Cite this article
Weikun Wang, Toric Sheaves on Hirzebruch Orbifolds. Doc. Math. 25 (2020), pp. 655–699DOI 10.4171/DM/758