LEADER 03621nam 2200529 a 450 001 9910739428303321 005 20200520144314.0 010 $a1-4614-6482-X 024 7 $a10.1007/978-1-4614-6482-2 035 $a(OCoLC)844350184 035 $a(MiFhGG)GVRL6VEX 035 $a(CKB)2670000000370503 035 $a(MiAaPQ)EBC1316989 035 $a(EXLCZ)992670000000370503 100 $a20130313d2013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 00$aBirational geometry, rational curves, and arithmetic /$fFedor Bogomolov, Brendan Hassett, Yuri Tschinkel, editors 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (ix, 319 pages) $cillustrations 225 0 $aSimons symposia 300 $aDescription based upon print version of record. 311 $a1-4939-0158-3 311 $a1-4614-6481-1 320 $aIncludes bibliographical references. 327 $aForeword -- Introduction.- A. Bertram and I. Coskun, The birational geometry of the Hilbert scheme of points on surfaces -- F. Bogomolov and Ch. Böhning, Isoclinism and stable cohomology of wreath products -- F. Bogomolov, I. Karzhemanov, and K. Kuyumzhiyan, Unirationality and existence of infinitely transitive models -- I. Cheltsov, L. Katzarkov, and V. Przyjalkowski, Birational geometry via moduli spaces -- O. Debarre, Curves of low degrees on projective varieties -- S. Kebekus, Uniruledness criteria and applications -- S. Kovács, The cone of curves of K3 surfaces revisited -- V. Lazi?, Around and beyond the canonical class -- C. Liedtke, Algebraic surfaces in positive characteristic -- A. Varilly-Alvarado, Arithmetic of Del Pezzo surfaces. 330 $aThis book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry.  It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions.  Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program. 410 0$aSimons Symposia. 606 $aGeometry, Algebraic 606 $aSurfaces, Algebraic 615 0$aGeometry, Algebraic. 615 0$aSurfaces, Algebraic. 676 $a516.35 701 $aBogomolov$b Fedor$0322148 701 $aHassett$b Brendan$0725397 701 $aTschinkel$b Yuri$066537 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910739428303321 996 $aBirational geometry, rational curves, and arithmetic$94196396 997 $aUNINA