Surfaces of general type with q=2 are rigidified
Algebraic Geometry
2017-12-07 v4
Abstract
Let be a minimal smooth projective surface of general type with irregularity . We show that, if has a nontrivial holomorphic automorphism acting trivially on the cohomology with rational coefficients, then it is a surface isogenous to a product. As a consequence of this geometric characterization, one infers that no nontrivial automorphism of surfaces of general type with (which are not necessarily minimal) can be homotopic to the identity. In particular, such surfaces are rigidified in the sense of Fabrizio Catanese.
Cite
@article{arxiv.1505.03929,
title = {Surfaces of general type with q=2 are rigidified},
author = {Wenfei Liu},
journal= {arXiv preprint arXiv:1505.03929},
year = {2017}
}
Comments
11 pages; Theorem 1.2 in the preliminary and Remark 3.2 are added; to appear in Communications in Contemporary Mathematics