摘要翻译：
补充提到了伊利耶夫-拉涅斯塔德和库兹涅佐夫的作品。----在第一部分，我们详细讨论了在属9的一般Fano 4-折叠上，四个秩为2的稳定向量丛的规范集的构造，并证明了它们是刚性的。伊利耶夫-拉涅斯塔德和库兹涅佐夫已经知道了这些结果，目的不同。在第二部分中，我们证明了它的各种线是P1×P1×P1×P1的超平面截面。然后我们计算了一个一般的Fano四重的周环，它在余维2上具有丰富的结构。4-丛给出了Grassmanian G(2,6）中的嵌入，并与E.Mezzeti和P.de Poi发现的一阶同余建立了联系。我们还将在这一部分中描述他们构造的非二次正规变量的归一化，以及它的平面立方变量的归一化，并详细描述这种情况下的zak对偶。
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英文标题：
《Geometry of genus 9 Fano 4-fold》
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作者：
Han Frederic
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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：
  References to the works of Iliev-Ranestad and Kuznetsov added.   -----   In a first part we detail the construction, on a general Fano 4-fold of genus 9, of a canonical set of four stable vector bundles of rank 2, and prove that they are rigid. Those results were already known by Iliev-Ranestad and Kuznetsov with different purposes.   In a second part we show that its variety of lines is an hyperplane section of P1xP1xP1xP1. Then we compute the Chow ring of a general Fano 4-fold, which appears to have a rich structure in codimension 2.   The 4-bundles gives embeddings in a Grassmannian G(2,6), and the link with the order one congruence discovered by E. Mezzeti and P de Poi is done. We will also describe in this part the normalization of the non quadraticaly normal variety they constructed, and also its variety of plane cubics and detail the zak duality in this case.
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PDF链接：
https://arxiv.org/pdf/0901.1054