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LEADER: 03643cam a2200385Ia 4500
001 5992049
005 20221121221520.0
008 060616t20072007maua b 001 0 eng d
020 $a0817644563
020 $a9780817644567
024 3 $a9780817644567
035 $a(OCoLC)ocm71747828
035 $a(NNC)5992049
035 $a5992049
040 $aNLGGC$efobidrtb$cNLGGC$dBAKER$dWTU$dOrLoB-B
090 $aQA607$b.K62 2007
100 1 $aKock, Joachim,$d1967-$0http://id.loc.gov/authorities/names/n2003010566
245 13 $aAn invitation to quantum cohomology :$bKontsevich's formula for rational plane curves /$cJoachim Kock, Israel Vainsencher.
246 30 $aKontsevich's formula for rational plane curves
260 $aBoston :$bBirkhäuser,$c[2007], ©2007.
300 $axii, 159 pages :$billustrations ;$c24 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aProgress in mathematics ;$vvol. 249
500 $aRevised and expanded translation of the original Portuguese edition (A fórmula de Kontsevich para curvas racionais planas. Rio de Janeiro : Instituto de Matemática Pura e Aplicada, c1999).
504 $aIncludes bibliographical references (p. [149]-155) and index.
505 00 $tPrologue : warming up with cross ratios, and the definition of moduli space -- $g1.$tStable n-pointed curves -- $g2.$tStable maps -- $g3.$tEnumerative geometry via stable maps -- $g4.$tGromov-Witten invariants -- $g5.$tQuantum cohomology.
520 1 $a"This 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 in 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 of 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 to 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."--BOOK JACKET.
650 0 $aGeometry, Enumerative.$0http://id.loc.gov/authorities/subjects/sh85054148
650 0 $aQuantum theory.$0http://id.loc.gov/authorities/subjects/sh85109469
650 0 $aHomology theory.$0http://id.loc.gov/authorities/subjects/sh85061770
650 0 $aCurves, Plane.$0http://id.loc.gov/authorities/subjects/sh85034926
700 1 $aVainsencher, Israel.$0http://id.loc.gov/authorities/names/n85379310
830 0 $aProgress in mathematics (Boston, Mass.) ;$vv. 249.$0http://id.loc.gov/authorities/names/n42019868
852 00 $bmat$hQA607$i.K62 2007g