Dualization invariance and a new complex elliptic genus

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Stefan Schreieder

External Research Organisations

  • Ludwig-Maximilians-Universität München (LMU)
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Details

Original languageEnglish
Pages (from-to)77-108
Number of pages32
JournalJournal fur die Reine und Angewandte Mathematik
Issue number692
Publication statusPublished - 1 Jul 2014
Externally publishedYes

Abstract

We define a new elliptic genus ψon the complex bordism ring. With coefficients in Z[1/2], we prove that it induces an isomorphism of the complex bordism ring modulo the ideal which is generated by all differences P (E) - P (E*) of projective bundles and their duals onto a polynomial ring on four generators in degrees 2, 4, 6 and 8. As an alternative geometric description of ψ we prove that it is the universal genus which is multiplicative in projective bundles over Calabi-Yau 3-folds.With the help of the q-expansion of modular forms we will see that for a complex manifold M, the value ψ (M) is a holomorphic Euler characteristic. We also compare ψ with Krichever-Höhn's complex elliptic genus and see that their only common specializations are Ochanine's elliptic genus and the Xy-genus.

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Cite this

Dualization invariance and a new complex elliptic genus. / Schreieder, Stefan.
In: Journal fur die Reine und Angewandte Mathematik, No. 692, 01.07.2014, p. 77-108.

Research output: Contribution to journal › Article › Research › peer review

Schreieder S. Dualization invariance and a new complex elliptic genus. Journal fur die Reine und Angewandte Mathematik. 2014 Jul 1;(692):77-108. doi: 10.1515/crelle-2012-0085
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