A VARIETY THAT CANNOT BE DOMINATED BY ONE THAT LIFTS

被引：1
|
作者：
de Bruyn, Remy van Dobben [1 ,2 ]
机构：
[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
[2] Inst Adv Study, Olden Lane, Princeton, NJ 08540 USA
来源：
DUKE MATHEMATICAL JOURNAL | 2021年 / 170卷 / 07期
关键词：
Algebraic Geometry; positive characteristic; finite fields; counterexamples; lifting; deformation theory; irrational pencils; algebraic surfaces of general type; 14G17; 14D15; 14D06; 14F35; 11G25; CLASSIFICATION; SURFACES; CONJECTURE; MANIFOLDS; CATANESE; ENRIQUES; MODULI;
D O I：
10.1215/00127094-2020-0055
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a strong version of a theorem of Siu and Beauville on morphisms to higher genus curves, and we use it to show that if a variety X in characteristic p lifts to characteristic 0, then any morphism X -> C to a curve of genus g >= 2 can be lifted along. We use this to construct, for every prime p, a smooth projective surface X over (F) over bar (p) that cannot be rationally dominated by a smooth proper variety Y that lifts to characteristic 0.
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页码：1251 / 1289
页数：39
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