Topics in Enumerative Algebraic Geometry Lecture 6
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چکیده
Today we shall discuss several examples of Gromov–Witten invariants, as well as some identities among them. We let X be a compact (almost-) Kähler manifold, and let Xg,n,d denote the moduli space of stable degree d maps into X of genus g curves with n marked points (q.v. the notes from previous lectures). Let us assume that we know what to make of [Xg,n,d]; as described last time, constructing the space Xg,n,d and defining its virtual fundamental class are quite nontrivial tasks. The Gromov–Witten invariants are introduced as follows: choose (t1, . . . , tn), with ti ∈ H (X), pull them back to Xg,n,d, take the cup product, and evaluate over the fundamental class:
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