发表机构
University of Pennsylvania（宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对横全纯叶状结构构造凝聚O_V模导出范畴的有限超联络模型，证明其与有界有限秩平坦V-超联络同伦范畴等价，还研究了下降性、单值群胚关联及全纯悬链相关性质。
AI 中文摘要
设X带有横全纯叶状结构，等价于椭圆对合结构V⊂T_CX，令O_V为其叶状常数、横全纯函数层。我们构造了凝聚O_V模的导出范畴的有限超联络模型。关键输入是混合de Rham–Dolbeault微分分次代数(∧^•V^∨,d_V)上有限Maurer–Cartan对象的混合局部约化：乘法同伦收缩实方向，之后Block的Dolbeault规范定理消除正横形式次数。对紧X，这给出有界有限秩平坦V-超联络的同伦范畴与D^b_coh(X,O_V)之间的正合等价，插值于de Rham与Dolbeault实现之间。我们在必要的一致振幅与秩界下证明了局部有限Čech下降，将凝聚心等同于横单值群胚上的等变凝聚解析层，并刻画了对普通和乐的下降。对全纯悬链，我们确定了整个超联络范畴（在Morita等价下）与横截Dolbeault范畴的同伦不动点，导出了等变Ext谱序列。S^1与S^2上的例子限定了普通单值1-群胚何时可恢复该导出范畴。
英文摘要
Let $X$ carry a transversely holomorphic foliation, equivalently an elliptic involutive structure $V\subset T_{\mathbb C}X$, and let ${\mathcal O}_V$ be its sheaf of leafwise-constant, transversely holomorphic functions. We construct a finite superconnection model for the derived category of coherent ${\mathcal O}_V$-modules. The key input is a mixed local reduction for finite Maurer--Cartan objects over the mixed de Rham--Dolbeault dga $(\wedge^\bullet V^\vee,d_V)$: a multiplicative homotopy contracts the real directions, after which Block's Dolbeault gauge theorem removes the positive transverse form degrees. For compact $X$, this gives an exact equivalence between the homotopy category of bounded finite-rank flat $V$-superconnections and $D^b_{\mathrm{coh}}(X,{\mathcal O}_V)$, interpolating between the de Rham and Dolbeault realizations. We prove locally finite Čech descent under necessary uniform amplitude and rank bounds, identify the coherent heart with equivariant coherent analytic sheaves on a transverse monodromy groupoid, and characterize descent to ordinary holonomy. For a holomorphic suspension, we identify the full superconnection category, up to Morita equivalence, with the homotopy fixed points of the Dolbeault category of the transversal and derive an equivariant Ext spectral sequence. Examples on $S^1$ and $S^2$ delimit when ordinary monodromy $1$-groupoids can recover the derived category.
Comments21 pages, no figures. Comments welcome!
