Titlebook: Birational Geometry, Rational Curves, and Arithmetic; Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel Book 2013 Springer Science+Business M

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The Birational Geometry of the Hilbert Scheme of Points on Surfaces,faces such as . and .. We discuss constructions of ample divisors and determine the ample cone for Hirzebruch surfaces and del Pezzo surfaces with ..≥2. As a corollary, we show that the Hilbert scheme of points on a Fano surface is a Mori dream space. We then discuss effective divisors on Hilbert sc

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Algebraic Surfaces in Positive Characteristic,miliar with characteristic-.-geometry but who would like to see similarities, as well as differences, to complex geometry. More precisely, these notes are on algebraic surfaces in positive characteristic and assume familiarity with the complex side of this theory, say, on the level of Beauville’s bo