Toric Sheaves on Hirzebruch Orbifolds
Weikun Wang
Department of Mathematics, University of Maryland, College Park, MD 20742, USA
![Toric Sheaves on Hirzebruch Orbifolds cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-25.png&w=3840&q=90)
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