Construction of the Moduli Space of Vector Bundles on an Orbifold Curve
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929397447000064 |
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| author | Das, Soumyadip Majumder, Souradeep |
| author_facet | Das, Soumyadip Majumder, Souradeep |
| contents | Let $k$ be an algebraically closed field of any characteristic, and let $(X,P)$ be an orbifold curve over $k$. We construct the moduli space $\mathrm{M}_{(X,P)}^{\mathrm{ss}}(n, Δ)$ of $P$-semistable bundles on $(X,P)$ of rank $n$ and determinant $Δ$. In the characteristic zero case, this result is well known and follows from GIT techniques. Our construction follows a different approach inspired by a GIT-free construction of Faltings. We show that when the moduli space is non-empty, it is a finite disjoint union of irreducible projective varieties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_16337 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of the Moduli Space of Vector Bundles on an Orbifold Curve Das, Soumyadip Majumder, Souradeep Algebraic Geometry 14A20, 14D20, 14D23 (Primary) 14F06, 14D22, 14G17 (Secondary) Let $k$ be an algebraically closed field of any characteristic, and let $(X,P)$ be an orbifold curve over $k$. We construct the moduli space $\mathrm{M}_{(X,P)}^{\mathrm{ss}}(n, Δ)$ of $P$-semistable bundles on $(X,P)$ of rank $n$ and determinant $Δ$. In the characteristic zero case, this result is well known and follows from GIT techniques. Our construction follows a different approach inspired by a GIT-free construction of Faltings. We show that when the moduli space is non-empty, it is a finite disjoint union of irreducible projective varieties. |
| title | Construction of the Moduli Space of Vector Bundles on an Orbifold Curve |
| topic | Algebraic Geometry 14A20, 14D20, 14D23 (Primary) 14F06, 14D22, 14G17 (Secondary) |
| url | https://arxiv.org/abs/2406.16337 |