Measure Preserving Holomorphic Vector Fields, Invariant Anti-Canonical Divisors and Gibbs Stability
Journal article, 2022

Let X be a compact complex manifold whose anti-canonical line bundle - K-X is big. We show that X admits no non-trivial holomorphic vector fields if it is Gibbs stable (at any level). The proof is based on a vanishing result for measure preserving holomorphic vector fields on X of independent interest. As an application it shown that, in general, if - K-X is big, there are no holomorphic vector fields on X that are tangent to a non-singular irreducible anti-canonical divisor S on X. More generally, the result holds for varieties with log terminal singularities and log pairs. Relations to a result of Berndtsson about generalized Hamiltonians and coercivity of the quantized Ding functional are also pointed out.

stability

holomorphic vector field

anti-canonical divisor

Author

Robert Berman

Chalmers, Mathematical Sciences, Algebra and geometry

Analysis Mathematica

0133-3852 (ISSN) 1588-273X (eISSN)

Vol. 48 2 347-375

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1007/s10476-022-0154-6

More information

Latest update

3/7/2024 9