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

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

Research output: Contribution to journalArticle

12 Citations (Scopus)

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
StatePublished - Jan 1 2013

Fingerprint

Lie groups
Calabi-Yau
4-manifold
Torus
Solvable Lie Groups
Symplectic Form
Fibration
Existence of Solutions
Simplify
Vary
Invariant
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Fino, A. ; Li, Yanyan ; Salamon, S. ; Vezzoni, L. / The Calabi-Yau equation on 4-manifolds over 2-Tori. In: Transactions of the American Mathematical Society. 2013 ; Vol. 365, No. 3. pp. 1551-1575.
@article{e355d7d89e6a4cb182bc792c64bfe497,
title = "The Calabi-Yau equation on 4-manifolds over 2-Tori",
abstract = "This paper pursues the study of the Calabi-Yau equation on certain symplectic non-K{\"a}hler 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-K{\"a}hler 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.",
author = "A. Fino and Yanyan Li and S. Salamon and L. Vezzoni",
year = "2013",
month = "1",
day = "1",
doi = "10.1090/S0002-9947-2012-05692-3",
language = "English (US)",
volume = "365",
pages = "1551--1575",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "3",

}

The Calabi-Yau equation on 4-manifolds over 2-Tori. / Fino, A.; Li, Yanyan; Salamon, S.; Vezzoni, L.

In: Transactions of the American Mathematical Society, Vol. 365, No. 3, 01.01.2013, p. 1551-1575.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The Calabi-Yau equation on 4-manifolds over 2-Tori

AU - Fino, A.

AU - Li, Yanyan

AU - Salamon, S.

AU - Vezzoni, L.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84871538039&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871538039&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2012-05692-3

DO - 10.1090/S0002-9947-2012-05692-3

M3 - Article

VL - 365

SP - 1551

EP - 1575

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 3

ER -