The Nef Cone Volume of Generalized Del Pezzo Surfaces
نویسندگان
چکیده
We compute a naturally defined measure of the size of the nef cone of a Del Pezzo surface. The resulting number appears in a conjecture of Manin on the asymptotic behavior of the number of rational points of bounded height on the surface. The nef cone volume of a Del Pezzo surface Y with (−2)-curves defined over an algebraically closed field is equal to the nef cone volume of a smooth Del Pezzo surface of the same degree divided by the order of the Weyl group of a simply-laced root system associated to the configuration of (−2)-curves on Y . When Y is defined over a non-closed field of characteristic 0, a similar result holds, except that the associated root system is no longer necessarily simply-laced.
منابع مشابه
A Nef Cone Volume for Generalized Del Pezzo Surfaces
For a smooth projective algebraic variety X , α(X) is a positive real number measuring the size of the dual to the cone of effective divisors on X . A conjecture of Manin predicts an asymptotic expression for the number of rational points of bounded height on X , in which the constant α(X) appears. Values of α(X) were found by Derenthal in [9] for split Del Pezzo surfaces, and also for split ge...
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