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An observation on $(-1)$-curves on rational surfaces


Authors: Olivia Dumitrescu and Brian Osserman
Journal: Proc. Amer. Math. Soc. 147 (2019), 1391-1398
MSC (2010): Primary 14J26
DOI: https://doi.org/10.1090/proc/14330
Published electronically: December 19, 2018
MathSciNet review: 3910406
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Abstract | References | Similar Articles | Additional Information

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.


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Additional 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
Article copyright: © Copyright 2018 American Mathematical Society