BIMEROMORPHIC GEOMETRY OF LCK MANIFOLDS

被引：1
|
作者：
Ornea, Liviu [1 ,2 ]
Verbitsky, Misha [3 ,4 ]
机构：
[1] Univ Bucharest, Fac Math & Informat, 14 Acad Str, Romani 70109, Romania
[2] Romanian Acad, Inst Math Simion Stoilow, 21 Calea Grivitei Str, Bucharest 010702, Romania
[3] Inst Nacl Matemat Pura & Aplicada IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil
[4] Natl Res Univ Higher Sch Econ, Fac Math, Lab Algebra Geometry, 6 Usacheva Str, Moscow, Russia
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 152卷 / 02期
关键词：
Locally conformally Ka.hler; global Ka.hler potential; bimeromorphism; minimal model; normal variety; KAHLER; SURFACES;
D O I：
10.1090/proc/16559
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A locally conformally Ka.hler (LCK) manifold is a complex manifold M which has a Ka.hler structure on its cover, such that the deck transform group acts on it by homotheties. Assume that the Ka.hler form is exact on the minimal Ka.hler cover of M. We prove that any bimeromorphic map M' -> M is in fact holomorphic; in other words, M has a unique minimal model. This can be applied to a wide class of LCK manifolds, such as the Hopf manifolds, their complex submanifolds and to OT manifolds.
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页码：701 / 707
页数：7
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