On surfaces with zero vanishing cycles

Abstract

We show that using an idea from a paper by Van de Ven one may obtain a simple proof of Zak's classification of smooth projective surfaces with zero vanishing cycles. This method of proof allows one to extend Zak's theorem to the case of finite characteristic.

arXiv comment8 pages, no figures. Version 2: added bibliographical references, minor changes in exposition. Version 3: proof of Proposition 2.3 corrected