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- W2467449870 abstract "For a curve $C$ of genus $6$ or $8$ and a torsion bundle $eta$ of order $ell$ we study the vanishing of the space of global sections of the twist $E_C otimes eta$ of the rank two Mukai bundle $E_C$ of $C$. The bundle $E_C$ was used in a well-known construction of Mukai which exhibits general canonical curves of low genus as sections of Grassmannians in the Plucker embedding. Globalizing the vanishing condition, we obtain divisors on the moduli spaces $overline{mathcal{R}}_{6,ell}$ and $overline{mathcal{R}}_{8,ell}$ of pairs $[C, eta]$. First we characterize these divisors by different conditions on linear series on the level curves, afterwards we calculate the divisor classes. As an application, we are able to prove that $overline{mathcal{R}}_{8,3}$ is of general type." @default.
- W2467449870 created "2016-07-22" @default.
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- W2467449870 date "2016-06-22" @default.
- W2467449870 modified "2023-09-27" @default.
- W2467449870 title "Twists of Mukai bundles and the geometry of the level $3$ modular variety over $overline{mathcal{M}}_8$" @default.
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