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arXiv · 1511.06618

A few questions about curves on surfaces

Ciro Ciliberto·Andreas Leopold Knutsen·John Lesieutre·Victor Lozovanu·Rick Miranda·Yusuf Mustopa·Damiano Testa
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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.

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Ciro Ciliberto, Andreas Leopold Knutsen, John Lesieutre, Victor Lozovanu, Rick Miranda, Yusuf Mustopa, Damiano Testa. 2015-11-20. A few questions about curves on surfaces. https://arxiv.org/abs/1511.06618

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