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摘要翻译：
研究了具有Chern多项式1+3T+6T2+4T3$的单秩6向量丛在$PP3$上的模空间$FM^s(6；3,6,4)$及其性质，特别是证明了有关其稳定性的部分结果。我们首先回顾这些束是如何与在$\pp^3$中构造六次节点曲面相关的，它具有一个由56个节点组成的偶数集合（参见\cite{CaTo}）。我们证明了与具有极小上同调的单丛对应的开集是维数19不可约的，并且是G.I.T的开集$\Fa^0$的双亚纯的。在$SL(W)\乘SL(U)$的自然作用下，$(3，3，4)$型三张量的射影空间$\fb:=\\b\in\pp(U^\ve\o乘W\o乘v^\vee)\}$的商空间。我们给出了这些束的几种构造，并将它们与3空间$\pp^3$中的三次曲面和对偶空间$(\pp^3)^{\vee}$中的三次曲面联系起来。由Igor Dolgachev提出的这些构造之一推广到其他类型的张量。此外，我们还将Cite{CaTo}中介绍的$(3,3,4)$-张量的{em交叉积对合}与$pp^3$中与三次曲面相关的Schur二次曲面联系起来，并进一步研究了这种对合的性质。
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英文标题：
《A remarkable moduli space of rank 6 vector bundles related to cubic
surfaces》
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作者：
Fabrizio Catanese (Universitaet Bayreuth), Fabio Tonoli (Universita'
di Trento)
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最新提交年份：
2007
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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：
We study the moduli space $\fM^s(6;3,6,4)$ of simple rank 6 vector bundles $\E$ on $\PP^3$ with Chern polynomial $1+3t+6t^2+4t^3$ and properties of these bundles, especially we prove some partial results concerning their stability. We first recall how these bundles are related to the construction of sextic nodal surfaces in $\PP^3$ having an even set of 56 nodes (cf. \cite{CaTo}). We prove that there is an open set, corresponding to the simple bundles with minimal cohomology, which is irreducible of dimension 19 and bimeromorphic to an open set $\fA^0$ of the G.I.T. quotient space of the projective space $\fB:=\{B\in \PP(U^\vee\otimes W\otimes V^\vee)\}$ of triple tensors of type $(3,3,4)$ by the natural action of $SL(W)\times SL(U)$. We give several constructions for these bundles, which relate them to cubic surfaces in 3-space $\PP^3$ and to cubic surfaces in the dual space $(\PP^3)^{\vee}$. One of these constructions, suggested by Igor Dolgachev, generalizes to other types of tensors. Moreover, we relate the socalled {\em cross-product involution} for $(3,3,4)$-tensors, introduced in \cite{CaTo}, with the Schur quadric associated to a cubic surface in $\PP^3$ and study further properties of this involution.
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PDF链接：
https://arxiv.org/pdf/0705.2184
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