Geodesic
Toric Sheaves on Hirzebruch Orbifolds
Documenta mathematica, Tome 25 (2020), pp. 655-699
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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​ obtained by projectivizing O⊕O(r) over the weighted projective line P(a,b). Next, we give a combinatorial description of toric sheaves on Hrab​ 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-stable torsion free sheaves of rank 1 and 2 on Hrab​. 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.
DOI : 10.4171/dm/758
Classification : 14D20, 14D23, 14M25
Mots-clés : toric orbifolds, moduli space of sheaves 
@article{10_4171_dm_758,
     author = {Weikun Wang},
     title = {Toric {Sheaves} on {Hirzebruch} {Orbifolds}},
     journal = {Documenta mathematica},
     pages = {655--699},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/758},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/758/}
}
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Weikun Wang. Toric Sheaves on Hirzebruch Orbifolds. Documenta mathematica, Tome 25 (2020), pp. 655-699. doi: 10.4171/dm/758

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