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arXiv · 1909.05899

Negative curves on special rational surfaces

Marcin Dumnicki·Lucja Farnik·Krishna Hanumanthu·Grzegorz Malara·Tomasz Szemberg·Justyna Szpond·Halszka Tutaj-Gasinska
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Abstract

We study negative curves on surfaces obtained by blowing up special configurations of points in the complex projective palne. Our main results concern the following configurations: very general points on a cubic, 3-torsion points on an elliptic curve and nine Fermat points. As a consequence of our analysis, we also show that the Bounded Negativity Conjecture holds for the surfaces we consider. The note contains also some problems for future attention.

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Marcin Dumnicki, Lucja Farnik, Krishna Hanumanthu, Grzegorz Malara, Tomasz Szemberg, Justyna Szpond, Halszka Tutaj-Gasinska. 2020-04-24. Negative curves on special rational surfaces. https://arxiv.org/abs/1909.05899

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