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摘要翻译：
根据前人的结果，实非奇异三次四重同调中复共轭引起的对合的共轭类决定了四重的射影等价和变形。在这里，我们展示了如何消除射影等价性，得到一个纯变形分类，即如何回答手性问题：哪些立方体不是变形等价于它们在镜面反射下的像。利用同调复共轭对合的本征子格给出了手性的一个算术判据，并以$m$-cubics（即实轨迹具有最丰富拓扑的那些）和$(M-1)$-cubics（关于实轨迹复杂性的下一种情况）为例，说明了该判据是如何有效地应用的。碰巧有一个$M$-cubics手征类和三个$(M-1)$-cubics手征类，与两个$M$-cubics非手征类和三个$(M-1)$-cubics非手征类相反。
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英文标题：
《On the deformation chirality of real cubic fourfolds》
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作者：
S.Finashin, V.Kharlamov
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最新提交年份：
2008
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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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一级分类：Mathematics 数学
二级分类：Geometric Topology 几何拓扑
分类描述：Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
流形，轨道，多面体，细胞复合体，叶状，几何结构
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英文摘要：
According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold up to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and to obtain a pure deformation classification, that is how to respond to the chirality question: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of chirality, in terms of the eigen-sublattices of the complex conjugation involution in homology, and show how this criterion can be effectively applied taking as examples $M$-cubics (that is those for which the real locus has the richest topology) and $(M-1)$-cubics (the next case with respect to complexity of the real locus). It happens that there is one chiral class of $M$-cubics and three chiral classes of $(M-1)$-cubics, contrary to two achiral classes of $M$-cubics and three achiral classes of $(M-1)$-cubics.
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PDF链接：
https://arxiv.org/pdf/0804.4882
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