Toric Sheaves on Hirzebruch Orbifolds

  • Weikun Wang

    Department of Mathematics, University of Maryland, College Park, MD 20742, USA
Toric Sheaves on Hirzebruch Orbifolds cover
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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 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. 655–699

DOI 10.4171/DM/758