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arXiv · 2412.18064

K-stability of Thaddeus' moduli of stable bundle pairs on genus two curves

Junyan Zhao
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Abstract

The moduli space of bundle stable pairs $\overline{M}_C(2,\Lambda)$ 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 $\overline{M}_C(2,\Lambda)$ to that of the moduli spaces of stable vector bundles $\overline{N}_C(2,\Lambda)$. In particular, Thaddeus' moduli spaces for genus two curves are all K-stable.

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Junyan Zhao. 2024-12-24. K-stability of Thaddeus' moduli of stable bundle pairs on genus two curves. https://arxiv.org/abs/2412.18064

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