On cubic fourfolds with an inductive structure
HTML articles powered by AMS MathViewer
- by Kenji Koike
- Proc. Amer. Math. Soc. 150 (2022), 3757-3769
- DOI: https://doi.org/10.1090/proc/15932
- Published electronically: May 13, 2022
- PDF | Request permission
Abstract:
We study the number of planes in four dimensional projective hypersurfaces which have so-called inductive structure. We also determine transcendental lattices of cubic fourfolds of this type.References
- Michela Artebani and Igor Dolgachev, The Hesse pencil of plane cubic curves, Enseign. Math. (2) 55 (2009), no. 3-4, 235–273. MR 2583779, DOI 10.4171/LEM/55-3-3
- Arnaud Beauville, Some surfaces with maximal Picard number, J. Éc. polytech. Math. 1 (2014), 101–116 (English, with English and French summaries). MR 3322784, DOI 10.5802/jep.5
- T. D. Browning and D. R. Heath-Brown, The density of rational points on non-singular hypersurfaces. II, Proc. London Math. Soc. (3) 93 (2006), no. 2, 273–303. With an appendix by J. M. Starr. MR 2251154, DOI 10.1112/S0024611506015784
- Samuel Boissière and Alessandra Sarti, Counting lines on surfaces, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), no. 1, 39–52. MR 2341513
- Araceli Bonifant and John Milnor, On real and complex cubic curves, Enseign. Math. 63 (2017), no. 1-2, 21–61. MR 3777131, DOI 10.4171/LEM/63-1/2-2
- Lucia Caporaso, Joe Harris, and Barry Mazur, How many rational points can a curve have?, The moduli space of curves (Texel Island, 1994) Progr. Math., vol. 129, Birkhäuser Boston, Boston, MA, 1995, pp. 13–31. MR 1363052, DOI 10.1007/978-1-4612-4264-2_{2}
- A. Degtyarev, I. Itenberg, and J. C. Ottem, Planes in cubic fourfolds, arXiv:2105.13951v1, 2021.
- Alex Degtyarev and Ichiro Shimada, On the topology of projective subspaces in complex Fermat varieties, J. Math. Soc. Japan 68 (2016), no. 3, 975–996. MR 3523534, DOI 10.2969/jmsj/06830975
- David Eisenbud and Joe Harris, 3264 and all that—a second course in algebraic geometry, Cambridge University Press, Cambridge, 2016. MR 3617981, DOI 10.1017/CBO9781139062046
- D. Mumford, On the equations defining abelian varieties. I, Invent. Math. 1 (1966), 287–354. MR 204427, DOI 10.1007/BF01389737
- Sławomir Rams and Matthias Schütt, 64 lines on smooth quartic surfaces, Math. Ann. 362 (2015), no. 1-2, 679–698. MR 3343894, DOI 10.1007/s00208-014-1139-y
- B. Segre, On arithmetical properties of quartic surfaces, Proc. London Math. Soc. (2) 49 (1947), 353–395. MR 21952, DOI 10.1112/plms/s2-49.5.353
- Tetsuji Shioda, The Hodge conjecture for Fermat varieties, Math. Ann. 245 (1979), no. 2, 175–184. MR 552586, DOI 10.1007/BF01428804
- Tetsuji Shioda and Toshiyuki Katsura, On Fermat varieties, Tohoku Math. J. (2) 31 (1979), no. 1, 97–115. MR 526513, DOI 10.2748/tmj/1178229881
- Tetsuji Shioda and Naoki Mitani, Singular abelian surfaces and binary quadratic forms, Classification of algebraic varieties and compact complex manifolds, Lecture Notes in Math., Vol. 412, Springer, Berlin, 1974, pp. 259–287. MR 0382289
- Claire Voisin, Some aspects of the Hodge conjecture, Jpn. J. Math. 2 (2007), no. 2, 261–296. MR 2342587, DOI 10.1007/s11537-007-0639-x
Bibliographic Information
- Kenji Koike
- Affiliation: Faculty of Education, University of Yamanashi, Takeda 4-4-37, Kofu, Yamanashi 400-8510, Japan
- MR Author ID: 670218
- Email: kkoike@yamanashi.ac.jp
- Received by editor(s): June 10, 2021
- Received by editor(s) in revised form: November 27, 2021, and December 1, 2021
- Published electronically: May 13, 2022
- Communicated by: Rachel Pries
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3757-3769
- MSC (2020): Primary 14J70
- DOI: https://doi.org/10.1090/proc/15932
- MathSciNet review: 4446227