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On the deformation chirality of real cubic fourfolds
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Date
2009-09-01
Author
Finashin, Sergey
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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 tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: 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, in contrast to two achiral classes of M-cubics and three achiral classes of (M - 1)-cubics.
Subject Keywords
Algebra and Number Theory
URI
https://hdl.handle.net/11511/42545
Journal
COMPOSITIO MATHEMATICA
DOI
https://doi.org/10.1112/s0010437x09004126
Collections
Department of Mathematics, Article
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S. Finashin, “On the deformation chirality of real cubic fourfolds,”
COMPOSITIO MATHEMATICA
, pp. 1277–1304, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42545.