The Calabi-Yau equation on 4-manifolds over 2-Tori

A. Fino, Y. Li, S. Salamon, L. Vezzoni

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

This paper pursues the study of the Calabi-Yau equation on certain symplectic non-Kähler 4-manifolds, building on a key example of Tosatti and Weinkove in which more general theory had proved less effective. Symplectic 4-manifolds admitting a 2-torus fibration over a 2-torus base T2 are modelled on one of three solvable Lie groups. Having assigned an invariant almost-Kähler structure and a volume form that effectively varies only on T2, one seeks a symplectic form with this volume. Our approach simplifies the previous analysis of the problem and establishes the existence of solutions in various other cases.

Original languageEnglish (US)
Pages (from-to)1551-1575
Number of pages25
JournalTransactions of the American Mathematical Society
Volume365
Issue number3
DOIs
Publication statusPublished - Jan 1 2013

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this