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Algebra i Analiz, 1999, Volume 11, Issue 5, Pages 100–125 (Mi aa1075)  

This article is cited in 29 scientific papers (total in 29 papers)

Research Papers

Elliptic genus of Calabi–Yau manifolds and Jacobi and Siegel modular forms

V. Gritsenkoab

a St. Petersburg Branch Steklov Mathematical Institute Russian Academy of Sciences, St. Petersburg, Russia
b Departement de Mathématique, Université de Lille, France

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English version:
St. Petersburg Mathematical Journal, 2000, 11:5, 781–804

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Received: 13.04.1999

Citation: V. Gritsenko, “Elliptic genus of Calabi–Yau manifolds and Jacobi and Siegel modular forms”, Algebra i Analiz, 11:5 (1999), 100–125; St. Petersburg Math. J., 11:5 (2000), 781–804

Citation in format AMSBIB
\by V.~Gritsenko
\paper Elliptic genus of Calabi--Yau manifolds and Jacobi and Siegel modular forms
\jour Algebra i Analiz
\yr 1999
\vol 11
\issue 5
\pages 100--125
\jour St. Petersburg Math. J.
\yr 2000
\vol 11
\issue 5
\pages 781--804

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    This publication is cited in the following articles:
    1. V. A. Gritsenko, V. V. Nikulin, “On classification of Lorentzian Kac–Moody algebras”, Russian Math. Surveys, 57:5 (2002), 921–979  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Lee Min Ho, “Jacobi-like forms and power series bundles”, Bull. Austral. Math. Soc., 66:2 (2002), 301–311  crossref  mathscinet  zmath  isi
    3. Spiridonov V.P., “An elliptic incarnation of the Bailey chain”, International Mathematics Research Notices, 2002, no. 37, 1945–1977  crossref  mathscinet  zmath  isi
    4. Borisov L., Libgober A., “Elliptic genera of singular varieties”, Duke Math. J., 116:2 (2003), 319–351  crossref  mathscinet  zmath  isi  scopus
    5. Nieper-Wißkirchen M.A., “On the elliptic genus of generalised Kummer varieties”, Math. Ann., 330:2 (2004), 201–213  crossref  mathscinet  zmath  isi  scopus
    6. Lee Min Ho, “Jacobi and modular forms on symmetric domains”, Rocky Mountain J. Math., 35:4 (2005), 1191–1204  crossref  mathscinet  zmath  isi  scopus
    7. Borisov L., Libgober A., “McKay correspondence for elliptic genera”, Annals of Mathematics, 161:3 (2005), 1521–1569  crossref  mathscinet  zmath  isi  scopus
    8. Libgober A., Szczesny M., “Discrete torsion, orbifold elliptic genera and the chiral de Rham complex”, Pure Appl. Math. Q., 2:4, part 2 (2006), 1217–1236  crossref  mathscinet  zmath  isi
    9. Dabholkar A., Narnpuri S., “Spectrum of dyons and black holes in CHL orbifolds using Borcherds lift”, J. High Energy Phys., 2007, no. 11, 077, 20 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    10. Gaberdiel M.R., Gukov S., Keller Ch.A., Moore G.W., Ooguri H., “Extremal N = (2,2) 2D conformal field theories”, Communications in Number Theory and Physics, 2:4 (2008), 743–801  crossref  mathscinet  zmath  isi  scopus
    11. Govindarajan S., Krishna K.G., “Generalized Kac-Moody algebras from CHL dyons”, J. High Energy Phys., 2009, no. 4, 032, 39 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    12. Eguchi T., Hikami K., “N=4 superconformal algebra and the entropy of hyperKahler manifolds”, Journal of High Energy Physics, 2010, no. 2, 019  crossref  mathscinet  zmath  isi  scopus
    13. Eguchi T., Hikami K., “N=2 Superconformal Algebra and the Entropy of Calabi-Yau Manifolds”, Letters in Mathematical Physics, 92:3 (2010), 269–297  crossref  mathscinet  zmath  adsnasa  isi  scopus
    14. Clery F., Gritsenko V., “Siegel modular forms of genus 2 with the simplest divisor”, Proc London Math Soc, 102:6 (2011), 1024–1052  crossref  mathscinet  zmath  isi  elib  scopus
    15. Govindarajan S., “Unravelling Mathieu Moonshine”, Nucl. Phys. B, 864:3 (2012), 823–839  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    16. Eguchi T., Hikami K., “Twisted Elliptic Genus for K3 and Borcherds Product”, Lett. Math. Phys., 102:2 (2012), 203–222  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    17. Cheng M.C.N., Duncan J.F.R., “The Largest Mathieu Group and (Mock) Automorphic Forms”, String-Math 2011, Proceedings of Symposia in Pure Mathematics, 85, eds. Block J., Distler J., Donagi R., Sharpe E., Amer Mathematical Soc, 2012, 53–82  crossref  mathscinet  adsnasa  isi
    18. Keller Ch.A., Ooguri H., “Modular Constraints on Calabi-Yau Compactifications”, Commun. Math. Phys., 324:1 (2013), 107–127  crossref  mathscinet  zmath  adsnasa  isi  scopus
    19. Clery F. Gritsenko V., “Modular Forms of Orthogonal Type and Jacobi Theta-Series”, Abh. Math. Semin. Univ. Hamburg, 83:2 (2013), 187–217  crossref  mathscinet  zmath  isi  scopus
    20. Persson D., Volpato R., “Second-Quantized Mathieu Moonshine”, Commun. Number Theory Phys., 8:3 (2014), 403–509  crossref  mathscinet  zmath  isi  elib  scopus
    21. Gritsenko V., Hulek K., “Uniruledness of Orthogonal Modular Varieties”, J. Algebr. Geom., 23:4 (2014), 711–725  crossref  mathscinet  zmath  isi  elib  scopus
    22. Cheng M.C.N., Duncan J.F.R., Harvey J.A., “Umbral Moonshine”, Commun. Number Theory Phys., 8:2 (2014), 101–242  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    23. Li P., “-1-Phenomena For the Pluri Chi(Y)-Genus and Elliptic Genus”, Pac. J. Math., 273:2 (2015), 331–351  crossref  mathscinet  zmath  isi  scopus
    24. Wong K., “Quarter-Bps States in Orbifold SIGMA Models With Ade Singularities”, J. High Energy Phys., 2017, no. 6, 116  crossref  mathscinet  zmath  isi  scopus
    25. Belin A., Castro A., Gomes J., Keller Ch.A., “Siegel Modular Forms and Black Hole Entropy”, J. High Energy Phys., 2017, no. 4, 057  crossref  mathscinet  isi  scopus
    26. Libgober A., “Elliptic Genus of Singular Algebraic Varieties and Quotients”, J. Phys. A-Math. Theor., 51:7 (2018), 073001  crossref  mathscinet  zmath  isi  scopus
    27. Gritsenko V., Wang H., “Powers of Jacobi Triple Product, Cohen'S Numbers and the Ramanujan Delta-Function”, Eur. J. Math., 4:2 (2018), 561–584  crossref  mathscinet  zmath  isi  scopus
    28. V. A. Gritsenko, “Reflective modular forms and applications”, Russian Math. Surveys, 73:5 (2018), 797–864  mathnet  crossref  crossref  adsnasa  isi  elib
    29. Belin A., Castro A., Gomes J., Keller Ch.A., “Siegel Paramodular Forms and Sparseness in Ads(3)/Cft2”, J. High Energy Phys., 2018, no. 11, 037  crossref  mathscinet  isi  scopus
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