English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Given a smooth genus two curve $C$, the moduli space SU$_C(3)$ of rank threesemi-stable vector bundles on $C$ with trivial determinant is a double cover in$\mathbb{P}^8$ branched over a sextic hypersurface, whose projective dual isthe famous Coble cubic, the unique cubic hypersurface that is singular alongthe Jacobian of $C$. In this paper we continue our exploration of theconnections of such moduli spaces with the representation theory of $GL_9$,initiated in \cite{GSW} and pursued in \cite{GS, sam-rains1, sam-rains2, bmt}.Starting from a general trivector $v$ in $\wedge^3\mathbb{C}^9$, we construct aFano manifold $D_{Z_{10}}(v)$ in $G(3,9)$ as a so-called orbital degeneracylocus, and we prove that it defines a family of Hecke lines in SU$_C(3)$. Wededuce that $D_{Z_{10}}(v)$ is isomorphic to the odd moduli space SU$_C(3,\mathcal{O}_C(c))$ of rank three stable vector bundles on $C$ with fixedeffective determinant of degree one. We deduce that the intersection of$D_{Z_{10}}(v)$ with a general translate of $G(3,7)$ in $G(3,9)$ is a K3surface of genus $19$.

Hecke cycles on moduli of vector bundles and orbital degeneracy loci