2019/11/12 by Hu, Wenchuan
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1911.04717
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.