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

[41] Some remarks on limit mixed Hodge structures and spectrum [J].

Dimca, Alexandru ;

Saito, Morihiko .

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2014, 22 (02) :69-78

[42] Higher order modular forms and mixed Hodge theory [J].

Sreekantan, Ramesh .

ACTA ARITHMETICA, 2009, 139 (04) :321-340

[43] 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

[44] CLASSIFYING SPACES OF DEGENERATING MIXED HODGE STRUCTURES, III: SPACES OF NILPOTENT ORBITS [J].

Kato, Kazuya ;

Nakayama, Chikara ;

Usui, Sampei .

JOURNAL OF ALGEBRAIC GEOMETRY, 2013, 22 (04) :671-772

[45] Hodge symmetry and decomposition on non-Kahler solvmanifolds [J].

Kasuya, Hisashi .

JOURNAL OF GEOMETRY AND PHYSICS, 2014, 76 :61-65

[46] TOPOLOGICAL RELATIONS ON WITTEN-KONTSEVICH AND HODGE POTENTIALS [J].

Kazarian, M. E. ;

Lando, S. K. .

MOSCOW MATHEMATICAL JOURNAL, 2012, 12 (02) :397-411

[47] Calabi-Yau Threefolds with Small Hodge Numbers [J].

Candelas, Philip ;

Constantin, Andrei ;

Mishra, Challenger .

FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS, 2018, 66 (06)

[48] Hodge theory and deformations of affine cones of subcanonical projective varieties [J].

Di Natale, Carmelo ;

Fatighenti, Enrico ;

Fiorenza, Domenico .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2017, 96 :524-544

[49] Spectral and Hodge theory of "Witt" incomplete cusp edge spaces [J].

Gell-Redman, Jesse ;

Swoboda, Jan .

COMMENTARII MATHEMATICI HELVETICI, 2019, 94 (04) :701-765

[50] A study of mirror symmetry through log mixed Hodge theory [J].

Usui, Sampei .

HODGE THEORY, COMPLEX GEOMETRY, AND REPRESENTATION THEORY, 2014, 608 :285-311

← 1 2 3 4 5 →