Duke Mathematical Journal
- Duke Math. J.
- Volume 166, Number 16 (2017), 3085-3145.
The Coolidge–Nagata conjecture
Let be a complex rational cuspidal curve contained in the projective plane. The Coolidge–Nagata conjecture asserts that is Cremona-equivalent to a line, that is, it is mapped onto a line by some birational transformation of . The second author recently analyzed the log minimal model program run for the pair , where is a minimal resolution of singularities, and as a corollary he proved the conjecture in the case when more than one irreducible curve in is contracted by the process of minimalization. We prove the conjecture in the remaining cases.
Duke Math. J., Volume 166, Number 16 (2017), 3085-3145.
Received: 3 November 2015
Revised: 5 February 2017
First available in Project Euclid: 13 July 2017
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Koras, Mariusz; Palka, Karol. The Coolidge–Nagata conjecture. Duke Math. J. 166 (2017), no. 16, 3085--3145. doi:10.1215/00127094-2017-0010. https://projecteuclid.org/euclid.dmj/1499911237