Moduli Spaces of Sheaves on Hirzebruch Orbifolds
| dc.contributor.advisor | Gholampour, Amin | en_US |
| dc.contributor.author | Wang, Weikun | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2019-09-27T05:37:54Z | |
| dc.date.available | 2019-09-27T05:37:54Z | |
| dc.date.issued | 2019 | en_US |
| dc.description.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 $\mathcal{H}_{r}^{ab}$ 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 $\mathcal{H}_{r}^{ab}$. Finally, we show that if $\mathcal{X}$ is the total space of the canonical bundle over a Hirzebruch orbifold, then we can obtain generating functions of Donaldson-Thomas invariants. | en_US |
| dc.identifier | https://doi.org/10.13016/jmaj-9onk | |
| dc.identifier.uri | http://hdl.handle.net/1903/25020 | |
| dc.language.iso | en | en_US |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.title | Moduli Spaces of Sheaves on Hirzebruch Orbifolds | en_US |
| dc.type | Dissertation | en_US |
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