On the biregular geometry of the Fulton-MacPherson compactification (Q1678137)

For a smooth projective variety \(X\), Let \(X[n]\) be the Fulton-MacPherson compactification of the configuration space of \(n\) ordered points on \(X\). In this paper the author studies the automorphism group Aut(\(X[n]\)) of \(X[n]\). When \(n\neq 2\) or \(\dim (X) \geq 2\), the author shows that the connected component of the identity of Aut(\(X[n]\)) is isomorphic to the connected component of the identity of Aut(\(X\)). When \(X\) is a curve \(C\) of genus \(\neq 1\), the author is able to compute the entire Aut(\(C[n]\)), and similarly for the case when \(X = C_1 \times \cdots \times C_r\) with the genus of \(C_i \geq 2\). Finally the author studies the automorphism groups of some Kontsevich moduli spaces of genus zero stable maps.