Fano hypersurfaces in positive characteristic

Yi Zhu

doi:10.5802/crmath.438

Research article - Algebraic geometry

Fano hypersurfaces in positive characteristic

Yi Zhu ¹

¹ United States

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 107-115.

Abstract

We prove that a general Fano hypersurface in a projective space over an algebraically closed field is separably rationally connected.

Received: 2022-02-22
Accepted: 2022-10-16
Revised after acceptance: 2022-11-15
Published online: 2024-02-02

DOI: 10.5802/crmath.438

Author's affiliations:

Yi Zhu ¹

¹ United States

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

@article{CRMATH_2024__362_G1_107_0,
     author = {Yi Zhu},
     title = {Fano hypersurfaces in positive characteristic},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {107--115},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.438},
     language = {en},
}

TY  - JOUR
AU  - Yi Zhu
TI  - Fano hypersurfaces in positive characteristic
JO  - Comptes Rendus. Mathématique
PY  - 2024
SP  - 107
EP  - 115
VL  - 362
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.438
LA  - en
ID  - CRMATH_2024__362_G1_107_0
ER  -

%0 Journal Article
%A Yi Zhu
%T Fano hypersurfaces in positive characteristic
%J Comptes Rendus. Mathématique
%D 2024
%P 107-115
%V 362
%I Académie des sciences, Paris
%R 10.5802/crmath.438
%G en
%F CRMATH_2024__362_G1_107_0

Yi Zhu. Fano hypersurfaces in positive characteristic. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 107-115. doi : 10.5802/crmath.438. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.438/

References
Cited by

[1] Dawei Chen; Izzet Coskun Towards Mori’s program for the moduli space of stable maps, Am. J. Math., Volume 133 (2011) no. 5, pp. 1389-1419 | DOI | MR | Zbl

[2] Tom Graber; Joe Harris; Jason M. Starr Families of rationally connected varieties, J. Am. Math. Soc., Volume 16 (2003) no. 1, pp. 57-67 | DOI | MR | Zbl

[3] Robin Hartshorne Algebraic geometry, Graduate Texts in Mathematics, 52, Springer, 1977 | DOI

[4] Aise J. de Jong; Jason M. Starr Every rationally connected variety over the function field of a curve has a rational point, Am. J. Math., Volume 125 (2003) no. 3, pp. 567-580 | DOI | MR | Zbl

[5] János Kollár Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, 32, Springer, 1996 | DOI

[6] János Kollár; Yoichi Miyaoka; Shigefumi Mori Rationally connected varieties, J. Algebr. Geom., Volume 1 (1992) no. 3, pp. 429-448 | MR | Zbl

[7] Jason M. Starr Arithmetic over function fields, Arithmetic geometry (Clay Mathematics Proceedings), Volume 8, American Mathematical Society, 2009, pp. 375-418 | MR | Zbl

Cited by Sources:

Comments - Policy