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001 978-0-8176-4495-6
003 DE-He213
005 20181204132646.0
007 cr nn 008mamaa
008 100301s2007 xxu| s |||| 0|eng d
020 _a9780817644956
_9978-0-8176-4495-6
024 7 _a10.1007/978-0-8176-4495-6
_2doi
040 _aISI Library, Kolkata
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
245 1 3 _aAn Invitation to Quantum Cohomology
_h[electronic resource] :
_bKontsevich’s Formula for Rational Plane Curves.
264 1 _aBoston, MA :
_bBirkhäuser Boston,
_c2007.
300 _aXIV, 162 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,
_x0743-1643 ;
_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 _aGeometry, algebraic.
650 0 _aK-theory.
650 0 _aMathematical physics.
650 0 _aAlgebraic topology.
650 0 _aGeometry.
650 0 _aMathematics.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aK-Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M11086
650 2 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aAlgebraic Topology.
_0http://scigraph.springernature.com/things/product-market-codes/M28019
650 2 4 _aGeometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21006
650 2 4 _aApplications of Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M13003
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817671129
776 0 8 _iPrinted edition:
_z9780817644567
830 0 _aProgress in Mathematics,
_x0743-1643 ;
_v249
856 4 0 _uhttps://doi.org/10.1007/978-0-8176-4495-6
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c425617
_d425617