Hyperkahler varieties as Brill-Noether loci on curves

Abstract: Consider the moduli space $M_C(r; K_C)$ of stable rank r vector bundles on a curve $C$ with canonical determinant, and let $h$ be the maximum number of linearly independent global sections of these bundles. If $C$ embeds in a K3 surface $X$ as a generator of $Pic(X)$ and the genus of $C$ is sufficiently high, I will show the Brill-Noether locus $BN_C \subset M_C(r; K_C)$ of bundles with $h$ global sections is a smooth projective Hyperkahler manifold, isomorphic to a moduli space of stable vector bundles on $X$. The main technique is to apply wall-crossing with respect to Bridgeland stability conditions on K3 surfaces.

algebraic geometry

Audience: researchers in the topic

( slides | video )

Comments: The synchronous discussion for Soheyla Feyzbakhsh’s talk is taking place not in zoom-chat, but at tinyurl.com/2022-05-27-sf (and will be deleted after ~3-7 days).

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Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

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