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- W2425101920 abstract "Consider a complete, connected, reduced curve C whose singularities are at worst nodes, n smooth numbered points x1, . . . , xn on C, and a morphism μ : C → Pr. According to Kontsevich, one says that the datum of C, x1, . . . , xn, and μ is a stable map if the following condition is satisfied. Let E be a smooth component of C such that μ(E) is a point; if the genus of E is zero (resp., one) then E contains at least three (resp., one) points which are among the xi or are singular in C but not in E. An isomorphism between stable maps (C, x1, . . . , xn, μ) and (C ???, x1, . . . , xn, μ???) is an isomorphism φ : C → C ??? such that φ(xi) = xi for i = 1, . . . , n and μ???φ = μ. A family of stable maps is a flat proper morphism f : C → S together with n sections σi : S → C, i = 1, . . . , n and a morphism μ : C → Pr such that, for every s ∈ S, (f(s),σ1(s), . . . ,σn(s), μ???f−1(s)) is a stable map. One has obvious notions of pullback and of isomorphism between families of stable maps." @default.
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- W2425101920 date "1995-01-01" @default.
- W2425101920 modified "2023-09-24" @default.
- W2425101920 title "A simple proof of the projectivity of Kontsevich's space of maps" @default.
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