000			03726nam a22005775i 4500
001			978-0-8176-4495-6
003			DE-He213
005			20251006084435.0
007			cr nn 008mamaa
008			100301s2007 xxu| s |||| 0|eng d
020			_a9780817644956
020			_a99780817644956
024	7		_a10.1007/978-0-8176-4495-6 _2doi
082	0	4	_a516.35 _223
100	1		_aKock, Joachim. _eauthor.
245	1	3	_aAn Invitation to Quantum Cohomology _h[electronic resource] : _bKontsevich's Formula for Rational Plane Curves / _cby Joachim Kock, Israel Vainsencher ; edited by Hyman Bass, Joseph Oesterlé, Alan Weinstein.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2007.
300			_aXII, 159 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProgress in Mathematics ; _v249
505	0		_aPrologue: Warming Up with Cross Ratios, and the Definition of Moduli Space -- Stable n-pointed Curves -- Stable Maps -- Enumerative Geometry via Stable Maps -- Gromov-Witten Invariants -- Quantum Cohomology.
520			_aThis book is an elementary introduction to stable maps and quantum cohomology, starting with an introduction to stable pointed curves, and culminating with a proof of the associativity of the quantum product. The viewpoint is mostly that of enumerative geometry, and the red thread of the exposition is the problem of counting rational plane curves. Kontsevich's formula is initially established in the framework of classical enumerative geometry, then as a statement about reconstruction for Gromov-Witten invariants, and finally, using generating functions, as a special case of the associativity of the quantum product. Emphasis is given throughout the exposition to examples, heuristic discussions, and simple applications of the basic tools to best convey the intuition behind the subject. The book demystifies these new quantum techniques by showing how they fit into classical algebraic geometry. Some familiarity with basic algebraic geometry and elementary intersection theory is assumed. Each chapter concludes with some historical comments and an outline of key topics and themes as a guide for further study, followed by a collection of exercises that complement the material covered and reinforce computational skills. As such, the book is ideal for self-study, as a text for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory. The book will prove equally useful to graduate students in the classroom setting as to researchers in geometry and physics who wish to learn about the subject.
650		0	_aMATHEMATICS.
650		0	_aGEOMETRY, ALGEBRAIC.
650		0	_aK-THEORY.
650		0	_aGEOMETRY.
650		0	_aALGEBRAIC TOPOLOGY.
650		0	_aMATHEMATICAL PHYSICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aALGEBRAIC GEOMETRY.
650	2	4	_aK-THEORY.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
650	2	4	_aALGEBRAIC TOPOLOGY.
650	2	4	_aGEOMETRY.
650	2	4	_aAPPLICATIONS OF MATHEMATICS.
700	1		_aVainsencher, Israel. _eauthor.
700	1		_aBass, Hyman. _eeditor.
700	1		_aOesterlé, Joseph. _eeditor.
700	1		_aWeinstein, Alan. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817644567
830		0	_aProgress in Mathematics ; _v249
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4495-6 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59672 _d59672