论文标题
Hyperkähler品种是曲线上的Brill-Noether基因座
Hyperkähler varieties as Brill-Noether loci on curves
论文作者
论文摘要
考虑使用规范决定簇在曲线$ c $上稳定的稳定等级r矢量捆绑包的模量空间$ m_c（r; k_c）$，而$ h $是这些捆绑包的线性独立全局部分的最大数量。 If $C$ embeds in a K3 surface $X$ as a generator of $Pic(X)$ and the genus $g$ of $C$ is sufficiently high, we show the Brill-Noether locus $BN_C \subset M_C(r; K_C)$ of bundles with $h$ global sections is a smooth projective Hyperkähler manifold of dimension $2g -2r \lfloor \ frac {g} {r} \ rfloor $，在$ x $上的稳定向量捆的模量空间。
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 $g$ of $C$ is sufficiently high, we show the Brill-Noether locus $BN_C \subset M_C(r; K_C)$ of bundles with $h$ global sections is a smooth projective Hyperkähler manifold of dimension $2g -2r \lfloor \frac{g}{r}\rfloor$, isomorphic to a moduli space of stable vector bundles on $X$.
