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- W4384264744 abstract "Given a smooth genus three curve $C$, the moduli space of rank two stable vector bundles on C with trivial determinant embeds in $mathbb{P}^8$ as a hypersurface whose singular locus is the Kummer threefold of $C$; this hypersurface is the Coble quartic. Gruson, Sam and Weyman realized that this quartic could be constructed from a general skew-symmetric fourform in eight variables. Using the lines contained in the quartic, we prove that a similar construction allows to recover SU$_C(2, L)$, the moduli space of rank two stable vector bundles on C with fixed determinant of odd degree L, as a subvariety of $G(2, 8)$. In fact, each point $p in C$ defines a natural embedding of SU$_C(2, mathcal{O}(p))$ in $G(2, 8)$. We show that, for the generic such embedding, there exists a unique quadratic section of the Grassmannian which is singular exactly along the image of SU$_C(2, mathcal{O}(p))$, and thus deserves to be coined the Coble quadric of the pointed curve $(C, p)$." @default.
- W4384264744 created "2023-07-14" @default.
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- W4384264744 date "2023-07-12" @default.
- W4384264744 modified "2023-10-17" @default.
- W4384264744 title "The Coble Quadric" @default.
- W4384264744 doi "https://doi.org/10.48550/arxiv.2307.05993" @default.
- W4384264744 hasPublicationYear "2023" @default.
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