A comparison of positivity in complex and tropical toric geometry

被引：2

作者：

Burgos Gil, Jose Ignacio ^{[1
]}

Gubler, Walter ^{[2
]}

Jell, Philipp ^{[2
]}

Kuennemann, Klaus ^{[2
]}

机构：

[1] UCM3, UCM, UAM, Inst Ciencias Matemat,CSIC, Calle Nicolas Cabrera 15, Madrid 28049, Spain

[2] Univ Regensburg, Math, D-93040 Regensburg, Germany

来源：

MATHEMATISCHE ZEITSCHRIFT | 2021年 / 299卷 / 3-4期

关键词：

Toric varieties; Tropicalization; Positive currents; Lagerberg forms;

D O I：

10.1007/s00209-021-02697-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a smooth complex toric variety we will compare real Lagerberg forms and currents on its tropicalization with invariant complex forms and currents on the toric variety. Our main result is a correspondence theorem which identifies the cone of invariant closed positive currents on the complex toric variety with closed positive currents on the tropicalization. In a subsequent paper, this correspondence will be used to develop a Bedford-Taylor theory of plurisubharmonic functions on the tropicalization.

引用

页码：1199 / 1255

页数：57

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