On Plane Cubics
نویسندگان
چکیده
منابع مشابه
The Enumerative Geometry of Plane Cubics. I: Smooth Cubics
We construct a variety of complete plane cubics by a sequence of five blow-ups over P9 . This enables us to translate the problem of computing characteristic numbers for a family of plane cubics into one of computing five Segre classes, and to recover classic enumerative results of Zeuthen and Maillard.
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Every automorphism of the complex projective plane P2 is linear and therefore behaves quite simply when iterated. It is natural to seek other rational complex surfaces—for instance, those obtained from P2 by successive blowing up—that admit automorphisms with more interesting dynamics. Until recently, very few examples with positive entropy seem to have been known (see e.g. the introduction to ...
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A well-known result of Beukers [3] on the generalized Ramanujan-Nagell equation has, at its heart, a lower bound on the quantity |x2 − 2n|. In this paper, we derive an inequality of the shape |x3 − 2n| ≥ x4/3, valid provided x3 6= 2n and (x, n) 6= (5, 7), and then discuss its implications for a variety of Diophantine problems.
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 1901
ISSN: 0024-6115
DOI: 10.1112/plms/s1-34.1.291