On lattice polarizable cubic fourfolds
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Publication:2105827
DOI10.1007/S40687-022-00368-6zbMATH Open1505.14090arXiv2103.09132OpenAlexW4311069181MaRDI QIDQ2105827
Author name not available (Why is that?)
Publication date: 8 December 2022
Published in: (Search for Journal in Brave)
Abstract: We extend non-emtpyness and irreducibility of Hassett divisors to the moduli spaces of -polarizable cubic fourfolds for higher rank lattices , which in turn provides a systematic approach for describing the irreducible components of intersection of Hassett divisors. We show that Fermat cubic fourfold is contained in every Hassett divisor, which yields a new proof of Hassett's existence theorem of special cubic fourfolds. We obtain an algorithm to determine the irreducible components of the intersection of any two Hassett divisors and we give new examples of rational cubic fourfolds. Moreover, we derive a numerical criterion for the algebraic cohomology of a cubic fourfold having an associated K3 surface and answer a question of Laza by realizing infinitely many rank lattices as the algebraic cohomologies of cubic fourfolds having no associated K3 surfaces.
Full work available at URL: https://arxiv.org/abs/2103.09132
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