03358nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184082001500207245011600222264004600338300003400384336002600418337002600444338003600470347002400506490003500530505021400565520156500779650001702344650002402361650001402385650002502399650002902424650001402453650002402467650001302491650001702504650002402521650001402545650003702559650002402596650001402620650003302634710003402667773002002701776003602721830003502757856004802792978-0-8176-4495-6DE-He21320180115171434.0cr nn 008mamaa100301s2007 xxu| s |||| 0|eng d a97808176449567 a10.1007/978-0-8176-4495-62doi 4aQA564-609 7aPBMW2bicssc 7aMAT0120102bisacsh04a516.3522313aAn Invitation to Quantum Cohomologyh[electronic resource] :bKontsevich’s Formula for Rational Plane Curves. 1aBoston, MA :bBirkhäuser Boston,c2007. aXIV, 162 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aProgress in Mathematics ;v2490 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. 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. 0aMathematics. 0aAlgebraic geometry. 0aK-theory. 0aApplied mathematics. 0aEngineering mathematics. 0aGeometry. 0aAlgebraic topology. 0aPhysics.14aMathematics.24aAlgebraic Geometry.24aK-Theory.24aMathematical Methods in Physics.24aAlgebraic Topology.24aGeometry.24aApplications of Mathematics.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780817644567 0aProgress in Mathematics ;v24940uhttp://dx.doi.org/10.1007/978-0-8176-4495-6