000			03624nam a22004815i 4500
001			978-1-4614-6482-2
003			DE-He213
005			20140220082825.0
007			cr nn 008mamaa
008			130517s2013 xxu| s |||| 0|eng d
020			_a9781461464822 _9978-1-4614-6482-2
024	7		_a10.1007/978-1-4614-6482-2 _2doi
050		4	_aQA564-609
072		7	_aPBMW _2bicssc
072		7	_aMAT012010 _2bisacsh
082	0	4	_a516.35 _223
100	1		_aBogomolov, Fedor. _eeditor.
245	1	0	_aBirational Geometry, Rational Curves, and Arithmetic _h[electronic resource] / _cedited by Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2013.
300			_aXII, 320 p. 21 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_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. Lazić, Around and beyond the canonical class -- C. Liedtke, Algebraic surfaces in positive characteristic -- A. Varilly-Alvarado, Arithmetic of Del Pezzo surfaces.
520			_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.
650		0	_aMathematics.
650		0	_aGeometry, algebraic.
650		0	_aGeometry.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aAlgebraic Geometry.
650	2	4	_aNumber Theory.
650	2	4	_aGeometry.
700	1		_aHassett, Brendan. _eeditor.
700	1		_aTschinkel, Yuri. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461464815
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-6482-2
912			_aZDB-2-SMA
999			_c95681 _d95681