Schubert varieties as variations of Hodge structure

被引：11

作者：

Robles, C. ^{[1
]}

机构：

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

SELECTA MATHEMATICA-NEW SERIES | 2014年 / 20卷 / 03期

基金：

美国国家科学基金会;

关键词：

Schubert variety; Variation of Hodge structure; Infinitesimal period relation; Griffiths' transversality; Hodge theory; Mumford-Tate group; LIE ALGEBRA COHOMOLOGY; INFINITESIMAL VARIATIONS; MANIFOLDS; INVARIANT; INTEGRALS; PERIODS;

D O I：

10.1007/s00029-014-0148-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We (1) characterize the Schubert varieties that arise as variations of Hodge structure (VHS); (2) show that the isotropy orbits of the infinitesimal Schubert VHS 'span' the space of all infinitesimal VHS; and (3) show that the cohomology classes dual to the Schubert VHS form a basis of the invariant characteristic cohomology associated with the infinitesimal period relation (a.k.a. Griffiths' transversality).

引用

页码：719 / 768

页数：50

共 50 条

[21] A GUIDE TO UNIPOTENT VARIATIONS OF MIXED HODGE STRUCTURE
HAIN, RM
ZUCKER, S
LECTURE NOTES IN MATHEMATICS, 1987, 1246 : 92 - 106
[22] VARIATIONS OF HODGE STRUCTURE, LEGENDRE SUBMANIFOLDS, AND ACCESSIBILITY
CARLSON, JA
TOLEDO, D
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 311 (01) : 391 - 411
[23] INFINITESIMAL VARIATIONS OF HODGE STRUCTURE .1.
CARLSON, J
GREEN, M
GRIFFITHS, P
HARRIS, J
COMPOSITIO MATHEMATICA, 1983, 50 (2-3) : 109 - 205
[24] THE POINCARE LEMMA FOR VARIATIONS OF POLARIZED HODGE STRUCTURE
KASHIWARA, M
KAWAI, T
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1987, 23 (02) : 345 - 407
[25] VARIATIONS OF POLARIZED HODGE STRUCTURE - ASYMPTOTICS AND MONODROMY
CATTANI, E
KAPLAN, A
SCHMID, W
LECTURE NOTES IN MATHEMATICS, 1987, 1246 : 16 - 31
[26] The Hodge star operator on Schubert forms
Künnemann, K
Tamvakis, H
TOPOLOGY, 2002, 41 (05) : 945 - 960
[27] INFINITESIMAL VARIATIONS OF HODGE STRUCTURE .2. AN INFINITESIMAL INVARIANT OF HODGE CLASSES
GRIFFITHS, P
HARRIS, J
COMPOSITIO MATHEMATICA, 1983, 50 (2-3) : 207 - 265
[28] Mixed Hodge Structure on Local Cohomology with Support in Determinantal Varieties
Perlman, Michael
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2024, 2024 (01) : 331 - 358
[29] Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures
Eyssidieux, Philippe
Simpson, Carlos
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2011, 13 (06) : 1769 - 1798
[30] Which Schubert Varieties are Hessenberg Varieties?
Escobar, Laura
Precup, Martha
Shareshian, John
TRANSFORMATION GROUPS, 2023,

← 1 2 3 4 5 →