Titlebook: An Invitation to Quantum Cohomology; Kontsevich‘s Formula Joachim Kock,Israel Vainsencher Textbook 2007 Birkh?user Boston 2007 Grad.algebra

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Prologue: Warming Up with Cross Ratios, and the Definition of Moduli Space,Throughout this book we work over the field of complex numbers. When we speak of schemes we mean schemes of finite type over Spec ?.

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,Gromov—Witten Invariants,The intersection numbers resulting from an ideal transverse situation as in Proposition 3.4.3. are the (genus-0) .. In Section 4.2 we establish the basic properties of Gromov-Witten invariants, and in 4.3 and 4.4 we describe recursive relations among them, allowing for their computation.

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Stable ,-pointed Curves,nherited from ., the important Deligne-Mumford-Knudsen moduli space of stable .-pointed rational curves which are the subject of this first chapter. We shall not go into the detail of the construction of ., but content ourselves with the cases .≤5. The combinatorics of the boundary deserves a carefu

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Quantum Cohomology,define a . on .. Kontsevich’s formula and the other recursions we found in Chapter 4, are then interpreted as partial differential equations for the Gromov-Witten potential. The striking fact about all these equations is that they amount to the associativity of the quantum product! In particular, Ko

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Conference proceedings 2016and Intelligent RecognitionSystems (SIRS-2015), December 16-19, 2015, Trivandrum, India. The programcommittee received 175 submissions. Each paper was peer reviewed by at leastthree or more independent referees of the program committee and the 59 paperswere finally selected. The papers offer stimula