Algebraicity of Hodge loci for variations of Hodge structure

被引：2

作者：

Cattani, Eduardo ^{[1
]}

Kaplan, Aroldo ^{[1
]}

机构：

[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01002 USA

来源：

HODGE THEORY, COMPLEX GEOMETRY, AND REPRESENTATION THEORY | 2014年 / 608卷

关键词：

INTEGRALS; MONODROMY; MANIFOLDS; PERIODS;

D O I：

10.1090/conm/608/12176

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

These notes are intended to be a companion to Cattani, Deligne, and Kaplan (1995), where the algebraicity of the loci of Hodge classes is proven without appealing to the Hodge conjecture. We give somewhat simplified proofs in the case of variations of Hodge structures over curves and surfaces which may help to clarify the arguments, and discuss some current generalizations, consequences and conjectures based on them.

引用

页码：59 / 83

页数：25

共 50 条

[31] Computing Heights via Limits of Hodge Structures [J].

Bloch, Spencer ;

de Jong, Robin ;

Sertoez, Emre Can .

EXPERIMENTAL MATHEMATICS, 2024, 33 (04) :547-558

[32] E1-degeneration of the irregular Hodge filtration [J].

Esnault, Helene ;

Sabbah, Claude ;

Yu, Jeng-Daw ;

Saito, Morihiko .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2017, 729 :171-227

[33] Periods and Hodge structures in perturbative quantum field theory [J].

Weinzierl, Stefan .

FEYNMAN AMPLITUDES, PERIODS AND MOTIVES, 2015, 648 :249-259

[34] Hodge genera and characteristic classes of complez algebraic varieties [J].

Cappell, Sylvain E. ;

Libgober, Anatoly ;

Maxim, Laurentiu ;

Shaneson, Julius L. .

ELECTRONIC RESEARCH ANNOUNCEMENTS IN MATHEMATICAL SCIENCES, 2008, 15 :1-7

[35] Hyperplane Arrangements and Mixed Hodge Numbers of the Milnor Fiber [J].

Kutler, Max ;

Usatine, Jeremy .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022, 2022 (11) :8644-8684

[36] THE HODGE CONJECTURE THE COMPLICATIONS OF UNDERSTANDING THE SHAPE OF GEOMETRIC SPACES [J].

Munoz, Vicente .

METODE SCIENCE STUDIES JOURNAL, 2018, (08) :51-57

[37] The Kapustin-Witten equations and nonabelian Hodge theory [J].

Liu, Chih-Chung ;

Rayan, Steven ;

Tanaka, Yuuji .

EUROPEAN JOURNAL OF MATHEMATICS, 2022, 8 (SUPPL 1) :23-41

[38] Hodge-GUE Correspondence and the Discrete KdV Equation [J].

Dubrovin, Boris ;

Liu, Si-Qi ;

Yang, Di ;

Zhang, Youjin .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2020, 379 (02) :461-490

[39] HODGE-THEORETIC MIRROR SYMMETRY FOR TORIC STACKS [J].

Coates, Tom ;

Corti, Alessio ;

Iritani, Hiroshi ;

Tseng, Hsian-Hua .

JOURNAL OF DIFFERENTIAL GEOMETRY, 2020, 114 (01) :41-115

[40] Hodge numbers for CICYs with symmetries of order divisible by 4 [J].

Candelas, Philip ;

Constantin, Andrei ;

Mishra, Challenger .

FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS, 2016, 64 (6-7) :463-509

← 1 2 3 4 5 →