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We give a complete description of the fourth tautological group of the moduli space of pointed stable curves, ${\bar{M}}_{g, n}$ , and prove that for $g \geq 8$ it coincides with the cohomology group with rational coefficients. We further give a conjectural upper bound depending on the genus for the degree of new tautological relations.

The geometry of the period mapping on cyclic covers of P1

Gonzalo Riera (1984)

Compositio Mathematica

The Hyperelliptic Locus with Special Reference to Characteristic Two.

Knud Lonsted (1976)

Mathematische Annalen

The Kodaira dimension of the moduli space of curves of genus ... 23.

D. Eisenbud, J. Harris (1987)

Inventiones mathematicae

The Lefshetz Vanishing Cycles on a Projective Nonsingular Plane Curve.

Bronislaw Wajnryb (1977)

Mathematische Annalen

The line bundles on moduli stacks of principal bundles on a curve.

Biswas, Indranil, Hoffmann, Norbert (2010)

Documenta Mathematica

The maximal rank conjecture for non-special curves in IP3.

E. Ballico, Ph. Ellia (1985)

Inventiones mathematicae

The moduli space of curves of genus two covering elliptic curves.

Naoki Murabayashi (1994)

Manuscripta mathematica

The moduli space of Riemann surfaces is Kähler hyperbolic.

McMullen, Curtis T. (2000)

Annals of Mathematics. Second Series

The Moduli Spaces of Vector Bundles over an Algebraic Curve.

S. Ramanan (1973)

Mathematische Annalen

The monodromy of Weierstrass points.

D. Eisenbud, J. Harris (1987)

Inventiones mathematicae

The Mumford conjecture

Geoffrey Powell (2004/2005)

Séminaire Bourbaki

The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space $B Γ_{\infty}$ derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that $B Γ_{\infty}$ admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...

The $p$ -rank stratification of Artin-Schreier curves

Rachel Pries, Hui June Zhu (2012)

Annales de l’institut Fourier

We study a moduli space ${𝒜𝒮}_{g}$ for Artin-Schreier curves of genus $g$ over an algebraically closed field $k$ of characteristic $p$ . We study the stratification of ${𝒜𝒮}_{g}$ by $p$ -rank into strata ${𝒜𝒮}_{g . s}$ of Artin-Schreier curves of genus $g$ with $p$ -rank exactly $s$ . We enumerate the irreducible components of ${𝒜𝒮}_{g, s}$ and find their dimensions. As an application, when $p = 2$ , we prove that every irreducible component of the moduli space of hyperelliptic $k$ -curves with genus $g$ and $2$ -rank $s$ has dimension $g - 1 + s$ . We also determine all pairs $(p, g)$ for...

The Picard group of the moduli of higher spin curves.

Jarvis, Tyler J. (2001)

The New York Journal of Mathematics [electronic only]

The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".

David Mumford, Finn Knudsen (1976)

Mathematica Scandinavica

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