A Characterization of Secant Varieties of Severi Varieties Among Cubic Hypersurfaces-Reference-Cited by-同舟云学术

A Characterization of Secant Varieties of Severi Varieties Among Cubic Hypersurfaces

Published:2020-12-22 Issue:4 Volume:2021 Page:2763-2782
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Fu Baohua¹,Jeong Yewon²,Zak Fyodor L³

Affiliation:

1. Hua Loo-Keng Laboratory of Mathematics and Morningside Center of Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190, China and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

2. Morningside Center of Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190, China

3. Central Economics Mathematical Institute of the Russian Academy of Sciences, Nakhimovskiǐ av. 47, Moscow 117418, Russia

Abstract

Abstract It is shown that an irreducible cubic hypersurface with nonzero Hessian and smooth singular locus is the secant variety of a Severi variety if and only if its Lie algebra of infinitesimal linear automorphisms admits a nonzero prolongation.

Funder

National Natural Science Foundation of China

Postdoctoral International Exchange Program of China

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/4/2763/36271315/rnaa223.pdf

Reference11 articles.

1. Classification of non-degenerate projective varieties with non-zero prolongation and application to target rigidity;Fu;Invent. Math.,2012

2. Special birational transformations of type $\left (2,1\right )$;Fu;J. Algebraic Geom.,2018

3. Cubic hypersurfaces with vanishing hessian;Gondim;J. Pure Appl. Algebra,2015

4. Prolongations of infinitesimal automorphisms of cubic hypersurfaces with nonzero Hessian;Hwang;Acta Math. Vietnam.,2020

5. Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under Kähler deformation;Hwang;Invent. Math.,2005