Nonexistence of Negative Curves
Abstract Let $X$ be the blowup of a weighted projective plane ${\mathbb {P}}(a,b,c)$ at a general point. The Kleiman–Mori cone of $X$ is two-dimensional with one ray generated by the class of the exceptional curve $E$. It is not known if the second extremal ray is always generated by the class of a...
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| Published in: | International mathematics research notices Vol. 2023; no. 16; pp. 14368 - 14400 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford University Press
01-08-2023
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| Online Access: | Get full text |
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| Summary: | Abstract
Let $X$ be the blowup of a weighted projective plane ${\mathbb {P}}(a,b,c)$ at a general point. The Kleiman–Mori cone of $X$ is two-dimensional with one ray generated by the class of the exceptional curve $E$. It is not known if the second extremal ray is always generated by the class of a curve. We construct an infinite family of projective toric surfaces of Picard number one such that their blowups $X$ at a general point have half-open Kleiman–Mori cones: there is no negative curve generating the other boundary ray of the cone. |
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| ISSN: | 1073-7928 1687-0247 |
| DOI: | 10.1093/imrn/rnac355 |