The projectivity of the moduli space of stable curves, II: The stacks $M_{g,n}$

Knudsen, Finn F.

doi:10.7146/math.scand.a-12001

Cited by 436 publications

(339 citation statements)

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“…, P r−2 ) where E is obtained by identifying the sections P r−1 and P r in an ordinary double point, and these sections are subsequently dropped from the labeling. Again, the morphism κ g;r is finite and unramified [18,Cor. 3.9].…”

Section: 2mentioning

confidence: 99%

Monodromy of the p-Rank Strata of the Moduli Space of Curves

Achter

Pries

2008

International Mathematics Research Notices

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ABSTRACT. We determine the Z/ℓ-monodromy and Z ℓ -monodromy of every irreducible component of the stratum M f g of curves of genus g and p-rank f in characteristic p. In particular, we prove that the Z/ℓ-monodromy of every component of M f g is the symplectic group Sp 2g (Z/ℓ) if g ≥ 3 and if ℓ is a prime distinct from p. The method involves results on the intersection of M f g with the boundary of M g . We give applications to the generic behavior of automorphism groups, Jacobians, class groups, and zeta functions of curves of given genus and p-rank.

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Section: 2mentioning

confidence: 99%

Monodromy of the p-Rank Strata of the Moduli Space of Curves

Achter

Pries

2008

International Mathematics Research Notices

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“…Historically, stable curves and stable pointed curves were introduced in order to construct in a natural way compactifications of moduli spaces (certainly the following names should be mentioned: Zariski, A. Mayer, Deligne, Mumford, Grothendieck, Knudsen, and many more). Among the vast amount of literature we mention only: [10], in this paper we find how stable curves can be used in order to compactify the moduli space of curves; see: [17], where stable pointed curves and families and moduli spaces of these are studied.…”

Section: Stable Pointed Curves (Following Deligne and Mumford Knudsenmentioning

confidence: 99%

“…In [17] the terminology "pointed stable curves" is used; however, we think we should make a distinction between pointed curves which are stable (as we defined above, following Knudsen) and stable curves which moreover have some marked points. Hence we prefer the terminology "stable pointed curves".…”

Section: Stable Pointed Curves (Following Deligne and Mumford Knudsenmentioning

confidence: 99%

Alterations can remove singularities

Oort

1998

Bull. Amer. Math. Soc.

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“…[4], [11]) and M g, [r] for the moduli stack of hyperbolic curves of type (g, r) over Z. Then we have a natural finiteétale Galois S r -covering M g,r → M g, [r] -where S r is the symmetric group on r letters.…”

Section: Notations and Conventionsmentioning

confidence: 99%

On Monodromically Full Points of Configuration Spaces of Hyperbolic Curves

Hoshi

2011

The Arithmetic of Fundamental Groups

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Abstract. In the present paper, we introduce and discuss the notion of monodromically full points of configuration spaces of hyperbolic curves. This notion leads to complements to M. Matsumoto's result concerning the difference between the kernels of the natural homomorphisms associated to a hyperbolic curve and its point from the Galois group to the automorphism and outer automorphism groups of the geometric fundamental group of the hyperbolic curve. More concretely, we prove that any hyperbolic curve over a number field has many "nonexceptional" closed points, i.e., closed points which do not satisfy a condition considered by Matsumoto, but that there exist infinitely many hyperbolic curves which admit many "exceptional" closed points, i.e., closed points which do satisfy the condition considered by Matsumoto. Moreover, we prove a Galois-theoretic characterization of equivalence classes of monodromically full points of configuration spaces, as well as a Galois-theoretic characterization of equivalence classes of quasimonodromically full points of cores. In a similar vein, we also prove a necessary and sufficient condition for quasi-monodromically full Galois sections of hyperbolic curves to be geometric.

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The projectivity of the moduli space of stable curves, II: The stacks $M_{g,n}$

Cited by 436 publications

References 0 publications

Monodromy of the p-Rank Strata of the Moduli Space of Curves

Monodromy of the p-Rank Strata of the Moduli Space of Curves

Alterations can remove singularities

On Monodromically Full Points of Configuration Spaces of Hyperbolic Curves

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