Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 087, 40 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.087
(Mi sigma433)
 

This article is cited in 10 scientific papers (total in 10 papers)

Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results

Mark Greena, James Carlsonb, Phillip Griffithsc

a University of California, Los Angeles, CA, United States
b Clay Mathematics Institute, United States
c The Institute for Advanced Study, Princeton, NJ, United States
References:
Abstract: This paper is a survey of the subject of variations of Hodge structure (VHS) considered as exterior differential systems (EDS). We review developments over the last twenty-six years, with an emphasis on some key examples. In the penultimate section we present some new results on the characteristic cohomology of a homogeneous Pfaffian system. In the last section we discuss how the integrability conditions of an EDS affect the expected dimension of an integral submanifold. The paper ends with some speculation on EDS and Hodge conjecture for Calabi–Yau manifolds.
Keywords: exterior differential systems; variation of Hodge structure, Noether–Lefschetz locus; period domain; integral manifold; Hodge conjecture; Pfaffian system; Chern classes; characteristic cohomology; Cartan–Kähler theorem.
Received: April 20, 2009; in final form August 31, 2009; Published online September 11, 2009
Bibliographic databases:
Document Type: Article
MSC: 14C30; 58A15
Language: English
Citation: Mark Green, James Carlson, Phillip Griffiths, “Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results”, SIGMA, 5 (2009), 087, 40 pp.
Citation in format AMSBIB
\Bibitem{GreCarGri09}
\by Mark Green, James Carlson, Phillip Griffiths
\paper Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results
\jour SIGMA
\yr 2009
\vol 5
\papernumber 087
\totalpages 40
\mathnet{http://mi.mathnet.ru/sigma433}
\crossref{https://doi.org/10.3842/SIGMA.2009.087}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2559674}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000271092200023}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84896060568}
Linking options:
  • https://www.mathnet.ru/eng/sigma433
  • https://www.mathnet.ru/eng/sigma/v5/p87
  • This publication is cited in the following 10 articles:
    1. Cecotti S., “Special Geometry and the Swampland”, J. High Energy Phys., 2020, no. 9, 147  crossref  mathscinet  isi  scopus
    2. Cacciatori S.L., Filippini S.A., “The E-3/Z(3) Orbifold, Mirror Symmetry, and Hodge Structures of Calabi-Yau Type”, J. Geom. Phys., 138 (2019), 70–89  crossref  mathscinet  zmath  isi  scopus
    3. Robles C., “Characteristic cohomology of the infinitesimal period relation”, Asian J. Math., 20:4 (2016), 725–758  crossref  mathscinet  zmath  isi  scopus
    4. Abraham D. Smith, “Constructing Involutive Tableaux with Guillemin Normal Form”, SIGMA, 11 (2015), 053, 14 pp.  mathnet  crossref  mathscinet
    5. Daniel J., Ma X., “Characteristic Laplacian in Sub-Riemannian Geometry”, Int. Math. Res. Notices, 2015, no. 24, 13290–13323  crossref  mathscinet  zmath  isi  scopus
    6. Robles C., “Schubert Varieties as Variations of Hodge Structure”, Sel. Math.-New Ser., 20:3 (2014), 719–768  crossref  mathscinet  zmath  isi  scopus
    7. Brevik J., Nollet S., “Developments in Noether-Lefschetz Theory”, Hodge Theory, Complex Geometry, and Representation Theory, Contemporary Mathematics, 608, eds. Doran R., Friedman G., Nollet S., Amer Mathematical Soc, 2014, 21–50  crossref  mathscinet  zmath  isi
    8. Kaplan A., Subils M., “on the Equivalence Problem For Bracket-Generating Distributions”, Hodge Theory, Complex Geometry, and Representation Theory, Contemporary Mathematics, 608, eds. Doran R., Friedman G., Nollet S., Amer Mathematical Soc, 2014, 157–171  crossref  mathscinet  zmath  isi
    9. Garbagnati A., Van Geemen B., “Examples of Calabi-Yau threefolds parametrised by Shimura varieties”, Rendiconti del Seminario Matematico, 68:3 (2010), 271–287  mathscinet  zmath
    10. Green M., Griffiths P., Kerr M., “Mumford-Tate domains”, Boll. Unione Mat. Ital. (9), 3:2 (2010), 281–307  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
     
      Contact us:
    math-net2025_01@mi-ras.ru
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025