Toric Sheaves on Hirzebruch Orbifolds

  • Weikun Wang

    Department of Mathematics, University of Maryland, College Park, MD 20742, USA
Toric Sheaves on Hirzebruch Orbifolds cover
Download PDF

This article is published open access.


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 Hrab\mathcal{H}_r^{ab} obtained by projectivizing OO(r)\mathcal{O} \oplus \mathcal{O}(r) over the weighted projective line P(a,b)\mathbb{P}(a,b). Next, we give a combinatorial description of toric sheaves on Hrab\mathcal{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\mu-stable torsion free sheaves of rank 11 and 22 on Hrab\mathcal{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\mathbb{P}(1,2) \times \mathbb{P}^1.

Cite this article

Weikun Wang, Toric Sheaves on Hirzebruch Orbifolds. Doc. Math. 25 (2020), pp. 655–699

DOI 10.4171/DM/758