Kodaira dimension of moduli of special cubic fourfolds

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Kodaira dimension of moduli of special cubic fourfolds. / Tanimoto, Sho; Varilly-Alvarado, Anthony.

In: Journal fuer die Reine und Angewandte Mathematik, Vol. 2019, No. 752, 2019, p. 265-300.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Tanimoto, S & Varilly-Alvarado, A 2019, 'Kodaira dimension of moduli of special cubic fourfolds', Journal fuer die Reine und Angewandte Mathematik, vol. 2019, no. 752, pp. 265-300. https://doi.org/10.1515/crelle-2016-0053

APA

Tanimoto, S., & Varilly-Alvarado, A. (2019). Kodaira dimension of moduli of special cubic fourfolds. Journal fuer die Reine und Angewandte Mathematik, 2019(752), 265-300. https://doi.org/10.1515/crelle-2016-0053

Vancouver

Tanimoto S, Varilly-Alvarado A. Kodaira dimension of moduli of special cubic fourfolds. Journal fuer die Reine und Angewandte Mathematik. 2019;2019(752):265-300. https://doi.org/10.1515/crelle-2016-0053

Author

Tanimoto, Sho ; Varilly-Alvarado, Anthony. / Kodaira dimension of moduli of special cubic fourfolds. In: Journal fuer die Reine und Angewandte Mathematik. 2019 ; Vol. 2019, No. 752. pp. 265-300.

Bibtex

@article{24bd2bd15fc143a7a4041a85eb5d7bb2,
title = "Kodaira dimension of moduli of special cubic fourfolds",
abstract = "A special cubic fourfold is a smooth hypersurface of degree 3 and dimension 4 that contains a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a countable family of Noether?Lefschetz divisors Cd in the moduli space C of smooth cubic fourfolds. These divisors are irreducible 19-dimensional varieties birational to certain orthogonal modular varieties. We use the ?low-weight cusp form trick? of Gritsenko, Hulek, and Sankaran to obtain information about the Kodaira dimension of Cd . For example, if d = 6n + 2, then we show that Cd is of general type for n > 18, n {20, 21, 25}; it has nonnegative Kodaira dimension if n > 13 and n ≠ 15. In combination with prior work of Hassett, Lai, and Nuer, our investigation leaves only twenty values of d for which no information on the Kodaira dimension of Cd is known. We discuss some questions pertaining to the arithmetic of K3 surfaces raised by our results.",
author = "Sho Tanimoto and Anthony Varilly-Alvarado",
year = "2019",
doi = "10.1515/crelle-2016-0053",
language = "English",
volume = "2019",
pages = "265--300",
journal = "Journal fuer die Reine und Angewandte Mathematik",
issn = "0075-4102",
publisher = "Walterde Gruyter GmbH",
number = "752",

}

RIS

TY - JOUR

T1 - Kodaira dimension of moduli of special cubic fourfolds

AU - Tanimoto, Sho

AU - Varilly-Alvarado, Anthony

PY - 2019

Y1 - 2019

N2 - A special cubic fourfold is a smooth hypersurface of degree 3 and dimension 4 that contains a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a countable family of Noether?Lefschetz divisors Cd in the moduli space C of smooth cubic fourfolds. These divisors are irreducible 19-dimensional varieties birational to certain orthogonal modular varieties. We use the ?low-weight cusp form trick? of Gritsenko, Hulek, and Sankaran to obtain information about the Kodaira dimension of Cd . For example, if d = 6n + 2, then we show that Cd is of general type for n > 18, n {20, 21, 25}; it has nonnegative Kodaira dimension if n > 13 and n ≠ 15. In combination with prior work of Hassett, Lai, and Nuer, our investigation leaves only twenty values of d for which no information on the Kodaira dimension of Cd is known. We discuss some questions pertaining to the arithmetic of K3 surfaces raised by our results.

AB - A special cubic fourfold is a smooth hypersurface of degree 3 and dimension 4 that contains a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a countable family of Noether?Lefschetz divisors Cd in the moduli space C of smooth cubic fourfolds. These divisors are irreducible 19-dimensional varieties birational to certain orthogonal modular varieties. We use the ?low-weight cusp form trick? of Gritsenko, Hulek, and Sankaran to obtain information about the Kodaira dimension of Cd . For example, if d = 6n + 2, then we show that Cd is of general type for n > 18, n {20, 21, 25}; it has nonnegative Kodaira dimension if n > 13 and n ≠ 15. In combination with prior work of Hassett, Lai, and Nuer, our investigation leaves only twenty values of d for which no information on the Kodaira dimension of Cd is known. We discuss some questions pertaining to the arithmetic of K3 surfaces raised by our results.

U2 - 10.1515/crelle-2016-0053

DO - 10.1515/crelle-2016-0053

M3 - Journal article

VL - 2019

SP - 265

EP - 300

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

SN - 0075-4102

IS - 752

ER -

ID: 142942429