Communications in Analysis and Geometry

Volume 27 (2019)

Number 2

Balanced metrics on uniruled manifolds

Pages: 329 – 355

DOI: https://dx.doi.org/10.4310/CAG.2019.v27.n2.a3

Authors

Ionuţ Chiose (Institute of Mathematics of the Romanian Academy, Bucharest, Romania)

Rareş Răsdeaconu (Department of Mathematics, Vanderbilt University, Nashville, Tennessee, U.S.A.)

Ioana Şuvaina (Department of Mathematics, Vanderbilt University, Nashville, Tennessee, U.S.A.)

Abstract

We show that an $n$-dimensional Moishezon manifold is uniruled if and only if it supports a balanced metric $\omega^{n-1}$ of positive total scalar Chern curvature. A similar statement also holds true for class $\mathscr{C}$ manifolds of dimension three.

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The first author was supported by the CNCS grant PN-II-ID-PCE-2011-3-0269 during the preparation of this work. The second author acknowledges the support of the Simons Foundation’s ”Collaboration Grant for Mathematicians”, Award #281266, while the third author was supported by the NSF grant DMS-1309029.

Received 20 August 2014

Accepted 10 February 2017

Published 23 August 2019