Analytic study of rational quintic surfaces having no multiple curves
نویسندگان
چکیده
منابع مشابه
K3 Surfaces, Rational Curves, and Rational Points
We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. Mathematics Subj...
متن کاملK3 Surfaces, Rational Curves, and Rational Points
We prove that for any of a wide class of elliptic surfaces X defined over a number field k, if there is an algebraic point on X that lies on only finitely many rational curves, then there is an algebraic point on X that lies on no rational curves. In particular, our theorem applies to a large class of elliptic K3 surfaces, which relates to a question posed by Bogomolov in 1981. Mathematics Subj...
متن کاملRational curves of degree 10 on a general quintic threefold
We prove the “strong form” of the Clemens conjecture in degree 10. Namely, on a general quintic threefold F in P, there are only finitely many smooth rational curves of degree 10, and each curve C is embedded in F with normal bundle O(−1) ⊕ O(−1). Moreover, in degree 10, there are no singular, reduced, and irreducible rational curves, nor any reduced, reducible, and connected curves with ration...
متن کاملCounting Curves on Rational Surfaces
In [CH3], Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number of fixed general points). We rephrase their arguments in the language of maps, and extend them to other rational surfaces, and other specified intersections with a divisor. As applications, (i) we count irreducible curves on Hirzebruc...
متن کاملRational curves on K3 surfaces
This document is based on lectures given at the 2007 NATO Advanced Study Institute on ‘Higher-Dimensional Geometry over Finite Fields’, organized at the University of Göttingen by Yuri Tschinkel, and on lectures given at the 2010 summer school ‘Arithmetic Aspects of Rational Curves’, organized at the Institut Fourier in Grenoble by Emmanuel Peyre. This work is supported in part by National Scie...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1932
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1932-05378-2