Search results for "Moduli space"

showing 5 items of 45 documents

MR 3020148 Reviewed McMullen, C.T. Braid groups and Hodge theory. Mathematische Annalen, vol. 355 (2013), pp.893–-946. (Reviewer Francesca Vetro) 20F…

2014

In this paper, the author studies the unitary representations of the braid group and the geometric structures on moduli space that arise via the Hodge theory of cyclic branched coverings of P^1. In particular, the author is interested in the classification of certain arithmetic subgroups of U(r, s) which envelop the image of the braid group. The author investigates their connections with complex reflection groups, Teichm\"{u}lller curves, ergodic theory and problems in surface topology.

braid groups cyclic branched coverings moduli spaces.Settore MAT/03 - Geometria
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A formula for the Euler characteristic of $\overline{{\cal M}}_{2,n}$

2001

In this paper we compute the generating function for the Euler characteristic of the Deligne-Mumford compactification of the moduli space of smooth n-pointed genus 2 curves. The proof relies on quite elementary methods, such as the enumeration of the graphs involved in a suitable stratification of \(\overline{{\cal M}}_{2,n}\).

euler characteristicOverlineGeneral MathematicsMathematical analysisStratification (mathematics)Moduli spaceCombinatoricssymbols.namesakeMathematics::Algebraic GeometryEuler characteristicsymbolsEnumerationSettore MAT/03 - GeometriaCompactification (mathematics)MathematicsMathematische Zeitschrift
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Euler Characteristics of Moduli Spaces of Curves

2005

Let ${mathcal M}_g^n$ be the moduli space of n-pointed Riemann surfaces of genus g. Denote by ${\bar {\mathcal M}}_g^n$ the Deligne-Mumford compactification of ${mathcal M}_g^n$. In the present paper, we calculate the orbifold and the ordinary Euler characteristic of ${\bar {\mathcal M}}_g^n$ for any g and n such that n>2-2g.

euler characteristicPure mathematicsModular equationApplied MathematicsGeneral MathematicsRiemann surfaceMathematical analysisModuli spaceModuli of algebraic curvesRiemann–Hurwitz formulasymbols.namesakeMathematics - Algebraic GeometryMathematics::Algebraic GeometryEuler characteristicGenus (mathematics)symbolsFOS: Mathematicsmoduli spaceAlgebraic Topology (math.AT)Compactification (mathematics)Settore MAT/03 - GeometriaMathematics - Algebraic TopologyAlgebraic Geometry (math.AG)Mathematics
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Combinatorics of Mumford-Morita-Miller classes in low genus

2003

Here we use elementary combinatorial arguments to give explicit formulae and relations for some cohomology classes of moduli spaces of stable curves of low genus.

rational cohomology classes moduli spaces of rational curvesSettore MAT/03 - Geometria
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Calculating cohomology groups of $overline M_0,n(mathbb P^r,d)$

2003

Here we investigate the rational cohomology of the moduli space ℳ̄0,n (ℙr,d) of degree d stable maps from n-pointed rational curves to ℙr. We obtain partial results for small values of d with an inductive method inspired by a paper of Enrico Arbarello and Maurizio Cornalba.

rational cohomology moduli space of stable mapsSettore MAT/03 - Geometria
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