A few questions about curves on surfaces
Algebraic Geometry
2015-11-23 v1
Abstract
In this note we address the following kind of question: let X be a smooth, irreducible, projective surface and D a divisor on X$satisfying some sort of positivity hypothesis, then is there some multiple of D depending only on X which is effective or movable? We describe some examples, discuss some conjectures and prove some results that suggest that the answer should in general be negative, unless one puts some really strong hypotheses either on D or on X.
Keywords
Cite
@article{arxiv.1511.06618,
title = {A few questions about curves on surfaces},
author = {Ciro Ciliberto and Andreas Leopold Knutsen and John Lesieutre and Victor Lozovanu and Rick Miranda and Yusuf Mustopa and Damiano Testa},
journal= {arXiv preprint arXiv:1511.06618},
year = {2015}
}
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8 pages