发表机构
University of Houston（休斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文分类了稳定向量丛模空间的Fourier-Mukai伙伴，并确定其导出自等价群，证明了亏格≥4时互素模空间导出等价当且仅当同构。
AI 中文摘要
我们分类了光滑射影Fourier-Mukai伙伴，并确定了稳定丛模空间$U_C(r,d)$的导出自等价群，其中$r\geq2$与$d$互素，曲线为光滑复射影曲线，假设$g(C)\geq3$且$\Aut(C)=1$。当Jacobian簇$J(C)$的自同态环为$\Z$时，伙伴由$(\Z/r\Z)^\times/\{\pm1\}$索引。我们还证明了亏格至少为四的复曲线上两个互素向量丛模空间导出等价当且仅当它们同构。
英文摘要
We classify the smooth projective Fourier--Mukai partners and determine the derived autoequivalence group of the moduli space $U_C(r,d)$ of stable bundles of coprime rank $r\geq2$ and degree $d$ on a smooth complex projective curve, assuming $g(C)\geq3$ and $\Aut(C)=1$. When the Jacobian $J(C)$ has endomorphism ring $\Z$, the partners are indexed by $(\Z/r\Z)^\times/\{\pm1\}$. We also prove that two coprime moduli spaces of vector bundles over complex curves of genus at least four are derived equivalent if and only if they are isomorphic.
Comments26 pages
