G的环面商n,2n

IF 0.8 4区数学 Q2 MATHEMATICS

Comptes Rendus Mathematique Pub Date : 2023-11-10 DOI:10.5802/crmath.501

Arpita Nayek, Pinakinath Saha

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引用次数: 0

摘要

设gn,2n是参数化2n的n维子空间的格拉斯曼函数。gn,2n的Picard群是由一个唯一的样本线束态(1)生成的。设T是SL(2n，)的极大环面，作用于gn,2n和态(1)。根据[10，定理3.10,p. 764]， 2是最小整数k，使得 (k)下降到GIT商。在本文中，我们证明了gn,2n (n≥3)by T关于态(2)=态(1)⊗2的GIT商随着态(2)的下降而极化时不是射影正态的。

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Torus quotient of the Grassmannian G n,2n

Let G n,2n be the Grassmannian parameterizing the n-dimensional subspaces of ℂ 2n . The Picard group of G n,2n is generated by a unique ample line bundle 𝒪(1). Let T be a maximal torus of SL(2n,ℂ) which acts on G n,2n and 𝒪(1). By [10, Theorem 3.10, p. 764], 2 is the minimal integer k such that 𝒪(k) descends to the GIT quotient. In this article, we prove that the GIT quotient of G n,2n (n≥3) by T with respect to 𝒪(2)=𝒪(1) ⊗2 is not projectively normal when polarized with the descent of 𝒪(2).

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来源期刊

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.