Geodesic
Toric Sheaves on Hirzebruch Orbifolds
Documenta mathematica, Tome 25 (2020), pp. 655-699.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $\mathcal{H}_r^{ab}$ obtained by projectivizing $\mathcal{O} \oplus \mathcal{O}(r)$ over the weighted projective line $\mathbb{P}(a,b)$. Next, we give a combinatorial description of toric sheaves on $\mathcal{H}_r^{ab}$ 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 $\mu $-stable torsion free sheaves of rank $1$ and $2$ on $\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 $\mathbb{P}(1,2) \times \mathbb{P}^1$.
Classification : 14D20, 14D23, 14M25
Keywords: toric orbifolds, moduli space of sheaves 
@article{DOCMA_2020__25__a49,
     author = {Wang, Weikun},
     title = {Toric {Sheaves} on {Hirzebruch} {Orbifolds}},
     journal = {Documenta mathematica},
     pages = {655--699},
     publisher = {mathdoc},
     volume = {25},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a49/}
}
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Wang, Weikun. Toric Sheaves on Hirzebruch Orbifolds. Documenta mathematica, Tome 25 (2020), pp. 655-699. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a49/