The automorphism group of M̄ g,n

2020

Journal of Algebra

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Moduli spaces of complete collineations are wonderful compactifications of spaces of linear maps of maximal rank between two fixed vector spaces. We investigate the birational geometry of moduli spaces of complete collineations and quadrics from the point of view of Mori theory. We compute their effective, nef and movable cones, the generators of their Cox rings, and their groups of pseudo-automorphisms. Furthermore, we give a complete description of both the Mori chamber and stable base locus decompositions of the effective cone of the space of complete collineations of the 3-dimensional projective space.

Section: Pseudo-automorphismsmentioning

confidence: 99%

On the birational geometry of spaces of complete forms II: Skew-forms

2020

Journal of Algebra

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“…By Remark 1.3 the remaining cases are covered by [Ma]. More precisely Aut(M 1,2 ) ∼ = (C * ) 2 , by [Ma,Proposition 3.8], and Aut(M g ) ∼ = Aut(M g,1 ) is the trivial group for g 2, by [Ma,Propositions 3.5,2.6].…”

Section: Automorphisms Of M Ga[n]mentioning

confidence: 99%

On the automorphisms of Hassett’s moduli spaces

Trans. Amer. Math. Soc.

Mella

2017

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Abstract. Let M g,A[n] be the moduli stack parametrizing weighted stable curves, and let M g,A[n] be its coarse moduli space. These spaces have been introduced by B. Hassett, as compactifications of Mg,n and Mg,n respectively, by assigning rational weights A = (a 1 , ..., an), 0 < a i 1 to the markings. In particular, the classical Deligne-Mumford compactification arises for a 1 = ... = an = 1. In genus zero some of these spaces appear as intermediate steps of the blow-up construction of M 0,n developed by M. Kapranov, while in higher genus they may be related to the LMMP on M g,n. We compute the automorphism groups of most of the Hassett's spaces appearing in the Kapranov's blow-up construction. Furthermore, if g 1 we compute the automorphism groups of all Hassett's spaces. In particular, we prove that if g 1 and 2g − 2 + n 3 then the automorphism groups of both M g,A [n] and M g,A[n] are isomorphic to a subgroup of Sn whose elements are permutations preserving the weight data in a suitable sense.

“…Finally, in Section 2.1 we apply the rigidity results in Section 2, and the techniques developed in [FM16, Section 1] to lift automorphisms from zero to positive characteristic, in order to extend the main results on the automorphism groups of Hassett spaces in [MM14], [MM16], [BM13], [Ma14] and [Ma16] over an arbitrary field.…”

Section: Introductionmentioning

confidence: 99%

On the rigidity of moduli of weighted pointed stable curves

Fantechi

Journal of Pure and Applied Algebra

2018

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Abstract. Let M g,A[n] be the Hassett moduli stack of weighted stable curves, and let M g,A [n] be its coarse moduli space. These are compactifications of Mg,n and Mg,n respectively, obtained by assigning rational weights A = (a1, ..., an), 0 < ai ≤ 1 to the markings; they are defined over Z, and therefore over any field. We study the first order infinitesimal deformations of M g,A [n] and M g,A [n] . In particular, we show that M 0,A[n] is rigid over any field, if g ≥ 1 then M g,A[n] is rigid over any field of characteristic zero, and if g + n > 4 then the coarse moduli space M g,A[n] is rigid over an algebraically closed field of characteristic zero. Finally, we take into account a degeneration of Hassett spaces parametrizing rational curves obtained by allowing the weights to have sum equal to two. In particular, we consider such a Hassett 3-fold which is isomorphic to the Segre cubic hypersurface in P 4 , and we prove that its family of first order infinitesimal deformations is non-singular of dimension ten, and the general deformation is smooth.