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natural fiber evaluation map of stable maps

Discussion in 'Mathematics' started by Jigar Famil, Oct 8, 2018.

  1. Jigar Famil

    Jigar Famil Guest

    I want to understand page 31 in FP-notes by Fulton and Pandharipande.

    Suppose that $K=D(A;B;D_1;D_2)$ be a boundry divisor of $\overline{M}_{0,n}(X,\beta)$ and let $\overline{M}_A=$ $\overline{M}_{0,A \cup \bullet}(X,\beta)$ where $\bullet$ is additional marking.let $e_A$ be evaluation map on $\bullet$.(Here $A$ is subset of $[n]$ and Suppose $\beta = \beta_1+\beta_2$)

    if $f:C \to X$ is moduli point in $\overline{M}_{0,A \cup \bullet}(X,\beta_1)$ how natural evaluation map $H^0(f^*{T_X}) \to T_X(f(\bullet))$ defined?

    I cant understand why do we have such a map?

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