On surfaces of general type with q=5
Algebraic Geometry
2010-04-01 v1
Abstract
We prove that a complex surface S with irregularity q(S)=5 that has no irrational pencil of genus >1 has geometric genus p_g(S)>7. As a consequence, one is able to classify minimal surfaces S of general type with q(S)=5 and p_g(S)<8. This result is a negative answer, for q=5, to the question asked in arXiv:0811.0390 of the existence of surfaces of general type with irregularity q>3 that have no irrational pencil of genus >1 and with the lowest possible geometric genus p_g=2q-3. This gives some evidence for the conjecture that the only irregular surface with no irrational pencil of genus >1 and p_g=2q-3 is the symmetric product of a genus three curve.
Keywords
Cite
@article{arxiv.1003.5991,
title = {On surfaces of general type with q=5},
author = {Margarida Mendes Lopes and Rita Pardini and Gian Pietro Pirola},
journal= {arXiv preprint arXiv:1003.5991},
year = {2010}
}
Comments
9 pages.