Characterization of Abelian Varieties
Algebraic Geometry
2007-05-23 v1
Abstract
We prove that any smooth complex projective variety X with plurigenera P1(X)=P2(X)=1 and irregularity q(X)=dim(X) is birational to an abelian variety.
Cite
@article{arxiv.math/9903184,
title = {Characterization of Abelian Varieties},
author = {Jungkai A. Chen and Christopher D. Hacon},
journal= {arXiv preprint arXiv:math/9903184},
year = {2007}
}
Comments
10 pages, amstex
Related papers
View all related →
Algebraic Geometry · Mathematics
Birational characterization of abelian varieties and ordinary abelian varieties in characteristic p>0
Christopher D. Hacon, Zsolt Patakfalvi, Lei Zhang
2019-07-17
Algebraic Geometry · Mathematics
Varieties with $P_2(X)=2$ and $q(X)=\dim X$
Zhi Jiang
2010-10-25
Algebraic Geometry · Mathematics
A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf II
Sho Ejiri, Akiyoshi Sannai
2017-08-30
Algebraic Geometry · Mathematics
Abelian varieties as automorphism groups of smooth projective varieties
Davide Lombardo, Andrea Maffei
2018-01-09
Algebraic Geometry · Mathematics
An Enriques Classification Theorem for Surfaces in Positive Characteristic
Eugenia Ferrari
2018-05-16
Algebraic Geometry · Mathematics
Effective characterization of ordinary abelian varieties, and beyond
Jefferson Baudin
2025-10-23
Algebraic Geometry · Mathematics
A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf
Akiyoshi Sannai, Hiromu Tanaka
2016-01-13
Algebraic Geometry · Mathematics
Effective characterization of quasi-abelian surfaces
Margarida Mendes Lopes, Rita Pardini, Sofia Tirabassi
2023-02-03
Algebraic Geometry · Mathematics
Holomorphic symmetric differentials and a birational characterization of Abelian Varieties
Ernesto C. Mistretta
2019-03-08
Algebraic Geometry · Mathematics
Enriques' characterization of Abelian surfaces in positive characteristic
Jefferson Baudin, Gebhard Martin
2026-05-20
Algebraic Geometry · Mathematics
Abelian varieties as automorphism groups of smooth projective varieties in arbitrary characteristics
Jérémy Blanc, Michel Brion
2021-05-24
Algebraic Geometry · Mathematics
Birational characterization of products of curves of genus 2
Christopher D. Hacon, Rita Pardini
2007-05-23
Algebraic Geometry · Mathematics
When is the diagonal contractible?
Xi Chen, Frank Gounelas
2025-07-30
Algebraic Geometry · Mathematics
Generic Vanishing Index and the Birationality of the Bicanonical Map of Irregular Varieties
Martí Lahoz
2011-11-29
Algebraic Geometry · Mathematics
Algebraic approximations of fibrations in abelian varieties over a curve
Hsueh-Yung Lin
2021-09-07
Algebraic Geometry · Mathematics
Rational points of varieties with ample cotangent bundle over function fields of positive characteristic
Henri Gillet, Damian Rössler
2017-06-27
Algebraic Geometry · Mathematics
Restriction of sections of abelian schemes
Najmuddin Fakhruddin
2007-05-23
Algebraic Geometry · Mathematics
On the birationality of the adjunction mapping of projective varieties
Andreas Leopold Knutsen
2011-09-13
Algebraic Geometry · Mathematics
Invariance of plurigenera of varieties with nonngative Kodaira dimensions
Hajime Tsuji
2016-09-07
alg-geom · Mathematics
On the cone of curves of an abelian variety
Thomas Bauer
2007-05-23
Algebraic Geometry · Mathematics
Birational rigidity and Q-factoriality of a singular double quadric
Constantin Shramov
2008-03-31
Algebraic Geometry · Mathematics
On quint-canonical birationality of irregular threefolds
Jheng-Jie Chen, Jungkai Alfred Chen, Meng Chen, Zhi Jiang
2020-06-17
Algebraic Geometry · Mathematics
On Mukai's conjecture for hyperelliptic varieties
Federico Caucci
2025-09-22
Algebraic Geometry · Mathematics
Algebraic varieties with quasi-projective universal cover
Benoît Claudon, Andreas Hoering, János Kollár
2011-02-15
Algebraic Geometry · Mathematics
On varieties with trivial tangent bundle
Kirti Joshi
2020-12-07