Holomorphic vector fields and rationality
Algebraic Geometry
2020-03-03 v3 Differential Geometry
Abstract
We show that a nonsingular complex projective variety admitting a holomorphic vector field with nonempty isolated zeroes, is rational using a key technique by Harvey-Lawson on finite volume flows. This statement was conjectured by J. Carrell. By the same technique, we obtain a uniform upper bound of Betti numbers of nonsingular complex projective variety admitting a holomorphic vector field with exact one zero point. Such an upper bound depends only on the dimension of the variety, which is a stronger version of a result of Akyildiz and Carrell.
Cite
@article{arxiv.1911.04717,
title = {Holomorphic vector fields and rationality},
author = {Wenchuan Hu},
journal= {arXiv preprint arXiv:1911.04717},
year = {2020}
}
Comments
10 pages. The proof of the main result is modified and upper bound of Betti numbers are given. Comments are welcome!