K-stability of Thaddeus' moduli of stable bundle pairs on genus two curves
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918311301742592 |
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| author | Zhao, Junyan |
| author_facet | Zhao, Junyan |
| contents | The moduli space of bundle stable pairs $\overline{M}_C(2,Λ)$ on a smooth projective curve $C$, introduced by Thaddeus, is a smooth Fano variety of Picard rank two. Focusing on the genus two case, we show that its K-moduli space is isomorphic to a GIT moduli of lines in quartic del Pezzo threefolds. Additionally, we construct a natural forgetful morphism from the K-moduli of $\overline{M}_C(2,Λ)$ to that of the moduli spaces of stable vector bundles $\overline{N}_C(2,Λ)$. In particular, Thaddeus' moduli spaces for genus two curves are all K-stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | K-stability of Thaddeus' moduli of stable bundle pairs on genus two curves Zhao, Junyan Algebraic Geometry The moduli space of bundle stable pairs $\overline{M}_C(2,Λ)$ on a smooth projective curve $C$, introduced by Thaddeus, is a smooth Fano variety of Picard rank two. Focusing on the genus two case, we show that its K-moduli space is isomorphic to a GIT moduli of lines in quartic del Pezzo threefolds. Additionally, we construct a natural forgetful morphism from the K-moduli of $\overline{M}_C(2,Λ)$ to that of the moduli spaces of stable vector bundles $\overline{N}_C(2,Λ)$. In particular, Thaddeus' moduli spaces for genus two curves are all K-stable. |
| title | K-stability of Thaddeus' moduli of stable bundle pairs on genus two curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2412.18064 |