论文标题
Mukai的K3表面非曲线曲线计划
Mukai's program for non-primitive curves on K3 surfaces
论文作者
论文摘要
Mukai的计划旨在通过将其作为曲线上的向量捆绑包的光彩范围的位点展示为Brill-Noether locus，以从任何曲线上恢复K3 Surface $ x $。如果$ x $具有第一张Picard，而曲线$ c \ in | h | $是原始的，则Feyzbakhsh确认了$ g \ geq 11 $和$ g \ neq 12 $。最近，Feyzbakhsh表明，$ x $上的某些模量稳定束的模量空间与curves的Brill-Noether curves of Curves in $ | h | $如果$ g $相当。在本文中，我们在非重要的充分线性系统$ | MH | $中与不可约曲线合作，并证明Mukai的程序在$ G \ neq 2 $，$ mg \ geq 11 $和$ mg \ $ mg \ neq \ neq \ neq 12 $时，对任何不可减至的曲线有效。此外，我们介绍了不稳定的地区，以改善Feyzbakhsh的分析。我们表明，每个维度都有Hyper-Kähler品种是曲线的Brill-Noether基因座。
Mukai's program seeks to recover a K3 surface $X$ from any curve $C$ on it by exhibiting it as a Fourier-Mukai partner to a Brill-Noether locus of vector bundles on the curve. In the case $X$ has Picard number one and the curve $C\in |H|$ is primitive, this was confirmed by Feyzbakhsh for $g\geq 11$ and $g\neq 12$. More recently, Feyzbakhsh has shown that certain moduli spaces of stable bundles on $X$ are isomorphic to the Brill-Noether locus of curves in $|H|$ if $g$ is sufficiently large. In this paper, we work with irreducible curves in a non-primitive ample linear system $|mH|$ and prove that Mukai's program is valid for any irreducible curve when $g\neq 2$, $mg\geq 11$ and $mg\neq 12$. Furthermore, we introduce the destabilising regions to improve Feyzbakhsh's analysis. We show that there are hyper-Kähler varieties as Brill-Noether loci of curves in every dimension.
