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摘要翻译：
众所周知，三次四重线的Fano格式是一个辛变体。我们通过在(2n-2)维n次超曲面Y上的Fano线格式上构造P=2n-4的闭P-形式来推广这一事实。我们通过Abel-Jacobi映射、Hochschild同调和链接类给出了这种形式的几个定义，并在n=4的情况下显式地计算了它。在Pfaffian超曲面Y的特殊情况下，我们证明了在同调射影对偶条件下自然产生的p维Calabi-Yau簇X上的Fano格式对某个模束空间是双分的，并且构造的形式是由X上的全纯体积形式导出的。对于一般的非Pfaffian超曲面，这是成立的，但对偶Calabi-Yau是不可交换的。
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英文标题：
《Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's》
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作者：
A. Kuznetsov, L. Manivel, D. Markushevich
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
It is well known that the Fano scheme of lines on a cubic 4-fold is a symplectic variety. We generalize this fact by constructing a closed p-form with p=2n-4 on the Fano scheme of lines on a (2n-2)-dimensional hypersurface Y of degree n. We provide several definitions of this form - via the Abel-Jacobi map, via Hochschild homology, and via the linkage class, and compute it explicitly for n = 4. In the special case of a Pfaffian hypersurface Y we show that the Fano scheme is birational to a certain moduli space of sheaves on a p-dimensional Calabi--Yau variety X arising naturally in the context of homological projective duality, and that the constructed form is induced by the holomorphic volume form on X. This remains true for a general non Pfaffian hypersurface but the dual Calabi-Yau becomes non commutative.
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PDF链接：
https://arxiv.org/pdf/0806.1154
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