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On the biregular geometry of the Fulton–MacPherson compactification.
- Source :
-
Advances in Mathematics . Dec2017, Vol. 322, p97-131. 35p. - Publication Year :
- 2017
-
Abstract
- Let X [ n ] be the Fulton–MacPherson compactification of the configuration space of n ordered points on a smooth projective variety X . We prove that if either n ≠ 2 or dim ( X ) ≥ 2 , then the connected component of the identity of Aut ( X [ n ] ) is isomorphic to the connected component of the identity of Aut ( X ) . When X = C is a curve of genus g ( C ) ≠ 1 we classify the dominant morphisms C [ n ] → C [ r ] , and thanks to this we manage to compute the whole automorphism group of C [ n ] , namely Aut ( C [ n ] ) ≅ S n × Aut ( C ) for any n ≠ 2 , while Aut ( C [ 2 ] ) ≅ S 2 ⋉ ( Aut ( C ) × Aut ( C ) ) . Furthermore, we extend these results on the automorphisms to the case where X = C 1 × . . . × C r is a product of curves of genus g ( C i ) ≥ 2 . Finally, using the techniques developed to deal with Fulton–MacPherson spaces, we study the automorphism groups of some Kontsevich moduli spaces M ‾ 0 , n ( P N , d ) . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 322
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 126119711
- Full Text :
- https://doi.org/10.1016/j.aim.2017.10.012