An observation on $(-1)$-curves on rational surfaces
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- by Olivia Dumitrescu and Brian Osserman
- Proc. Amer. Math. Soc. 147 (2019), 1391-1398
- DOI: https://doi.org/10.1090/proc/14330
- Published electronically: December 19, 2018
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Abstract:
We give an effective iterative characterization of the classes of (smooth, rational) $(-1)$-curves on the blowup of the projective plane at general points. Such classes are characterized as having self-intersection $-1$, arithmetic genus $0$, and intersecting every $(-1)$-curve of smaller degree nonnegatively.References
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Bibliographic Information
- Olivia Dumitrescu
- Affiliation: Department of Mathematics, Central Michigan University, Mount Pleasant, Michigan 48859
- MR Author ID: 889839
- Brian Osserman
- Affiliation: Department of Mathematics, University of California, Davis, Davis, California 95616
- MR Author ID: 722512
- Received by editor(s): March 7, 2018
- Received by editor(s) in revised form: June 29, 2018
- Published electronically: December 19, 2018
- Additional Notes: The second author was partially supported by a grant from the Simons Foundation #279151.
- Communicated by: Rachel Pries
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 1391-1398
- MSC (2010): Primary 14J26
- DOI: https://doi.org/10.1090/proc/14330
- MathSciNet review: 3910406