Rational cubic fourfolds with a symplectic group of automorphisms
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912576582975488 |
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| author | Pedrini, Claudio |
| author_facet | Pedrini, Claudio |
| contents | A well known conjecture asserts that a cubic fourfold X is rational if it has a cohomologically associated K3 surface. G.Ouchi proved that if X admits a finite group G of symplectic automorphisms, whose order is different from 2, then X has an associated K3 surface S in the derived sense.This is equivalent to have a cohomologically associated K3 surface and therefore X is conjecturally rational. In this note we prove that cubic fourfolds with a cyclic group of symplectic automorphisms whose order is not a power of 2, are rational and belong to the Hassett divisor C_d, with d = 14, 42. We also describe rational cubic fourfolds X with a symplectic group of automorphisms G, such that (G, S_G(X), is a Lech pair where th rank of S_G equals 19 or 20. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational cubic fourfolds with a symplectic group of automorphisms Pedrini, Claudio Algebraic Geometry A well known conjecture asserts that a cubic fourfold X is rational if it has a cohomologically associated K3 surface. G.Ouchi proved that if X admits a finite group G of symplectic automorphisms, whose order is different from 2, then X has an associated K3 surface S in the derived sense.This is equivalent to have a cohomologically associated K3 surface and therefore X is conjecturally rational. In this note we prove that cubic fourfolds with a cyclic group of symplectic automorphisms whose order is not a power of 2, are rational and belong to the Hassett divisor C_d, with d = 14, 42. We also describe rational cubic fourfolds X with a symplectic group of automorphisms G, such that (G, S_G(X), is a Lech pair where th rank of S_G equals 19 or 20. |
| title | Rational cubic fourfolds with a symplectic group of automorphisms |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.06817 |