The Kodaira dimension of moduli spaces of curves with marked points

Logan, Adam

doi:10.1353/ajm.2003.0005

Cited by 88 publications

(84 citation statements)

References 14 publications

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“…The class of these pointed divisors has been calculated in many special cases, in particular in [34] and later by Farkas in [18]. We collect the results that are needed here.…”

Section: Special Divisors On Moduli Spacesmentioning

confidence: 99%

“…If jwj D g D d and r D 1 the class of the Brill-Noether divisor was calculated in [34,Theorem 5.4]. It has class…”

Section: Special Divisors On Moduli Spacesmentioning

confidence: 99%

“…The intersection number B 2 Nfold.2/ can also be calculated using [34,Proposition 3.4] by setting a 1 D 1; a 2 D 2; g D 5; h D 1, and it equals 50. This equals Logan's counting, since in the pair .p 2 ; q 1 / now p 2 has weight 2, which distinguishes it from q 1 .…”

Section: Special Divisors On Moduli Spacesmentioning

confidence: 99%

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Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus

Chen

Möller

2012

Geom. Topol.

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We show that for many strata of Abelian differentials in low genus the sum of Lyapunov exponents for the Teichmüller geodesic flow is the same for all Teichmüller curves in that stratum, hence equal to the sum of Lyapunov exponents for the whole stratum. This behavior is due to the disjointness property of Teichmüller curves with various geometrically defined divisors on moduli spaces of curves.

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“…The class of these pointed divisors has been calculated in many special cases, in particular in [34] and later by Farkas in [18]. We collect the results that are needed here.…”

Section: Special Divisors On Moduli Spacesmentioning

confidence: 99%

“…If jwj D g D d and r D 1 the class of the Brill-Noether divisor was calculated in [34,Theorem 5.4]. It has class…”

Section: Special Divisors On Moduli Spacesmentioning

confidence: 99%

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Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus

Chen

Möller

2012

Geom. Topol.

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“…As shown in [5], all these spaces are rational, so the base of the induction holds true. Finally, when g ≥ 2 and p > d (g, n), M g,n is a unirational variety; see [26], Theorem 7.1. Hence, from a dominant rational map…”

Section: Theorem 1 Let G and N Be Non-negative Integersmentioning

confidence: 99%

Moduli of curves and spin structures via algebraic geometry

Bini

Fontanari

2006

Trans. Amer. Math. Soc.

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Abstract. Here we investigate some birational properties of two collections of moduli spaces, namely moduli spaces of (pointed) stable curves and of (pointed) spin curves. In particular, we focus on vanishings of Hodge numbers of type (p, 0) and on computations of Kodaira dimension. Our methods are purely algebro-geometric and rely on an induction argument on the number of marked points and the genus of the curves.

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“…[HMu,Harr,EH,Far,Lo,V,CT,CC2]. In contrast, little is known about higher codimension cycles on M g,n , in part because their positivity properties are not as well-behaved.…”

Section: Introductionmentioning

confidence: 99%

Extremal higher codimension cycles on moduli spaces of curves

Chen¹,

Coskun²

2015

Proc. London Math. Soc.

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Abstract. We show that certain geometrically defined higher codimension cycles are extremal in the effective cone of the moduli space Mg,n of stable genus g curves with n ordered marked points. In particular, we prove that codimension two boundary strata are extremal and exhibit extremal boundary strata of higher codimension. We also show that the locus of hyperelliptic curves with a marked Weierstrass point in M3,1 and the locus of hyperelliptic curves in M4 are extremal cycles. In addition, we exhibit infinitely many extremal codimension two cycles in M1,n for n ≥ 5 and in M2,n for n ≥ 2.

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The Kodaira dimension of moduli spaces of curves with marked points

Abstract: We sharpen our previous results on the g and n such that M g,n is of general type for some g with g + 1 prime.

Cited by 88 publications

References 14 publications

Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus

Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus

Moduli of curves and spin structures via algebraic geometry

Extremal higher codimension cycles on moduli spaces of curves

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