The open set parameterizes stable curves of genus g having at most k rational components. By the work of Looijenga, one expects that the cohomological excess of is at most g1+k. In this paper, we show that when k=0, the conjectured upper bound is sharp by showing that there is a ...
arbitrary schemes and show how moduli spaces of pointed curves of genus zero like the Grothendieck-Knudsen moduli spaces $\\overline{M}_{0,n}$ and the Losev-Manin moduli spaces $\\overline{L}_n$ can be interpreted as inverse limits of moduli spaces of representations of certain bipartite ...
Planofthispaper:Inthefollowingsection,werevisebasicfactson weightedpointedcurvesofgenuszero,theirmodulispaceM A ,andthecom- binatorialstratificationofM A .InSection3,weconsiderrestrictionsof forgetfulmorphismstothestrataofM A andstudytheirfibers.Wecalculate therelativehomologyofthestratainductivelybyusingfo...
The moduli space Mg of curves of fixed genus g that is, the algebraic variety that parametrizes all curves of genus g is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent de...
We describe the singular locus of the compactification of the moduli space$R_{g,l}$ of curves of genus $g$ paired with an $l$-torsion point in theirJacobian. Generalising previous work for $l\\le 2$, we also describe thesublocus of noncanonical singularities for any positive integer $l...
Farkas,Gavril - 《American Journal of Mathematics》 被引量: 116发表: 2009年 Algebraic and tropical curves: comparing their moduli spaces We construct the moduli space for equivalence classes of n-pointed tropical curves of genus g, together with its compactification given by weighted tropica... L...
The purpose of this paper is to prove that the moduli space JC/g of curves of genus g over C is of general type if g is odd and g> 25. Moreover, the Kodaira dimension is at least 0 if g=23. It appears that a variant of our technique, which is technically more difficult, will...
In this paper we give an explicit construction of the moduli space of the pointed complete Gorenstein curves of arithmetic genus g with a given quasi-symmetric Weierstrass semigroup, that is, a Weierstrass semigroup whose last gap is equal to 2g – 2. We identify such a curve with its imag...
Here we focus on the compactification of the moduli space of curves of genus g together with an unramified double cover, constructed by Arnaud Beauville in order to compactify the Prym mapping. We present an alternative description of it, inspired by the moduli space of spin curves of Maurizi...
We prove that the coarse moduli space of curves of genus six is birational to an arithmetic quotient of a bounded symmetric domain of type IV by giving a period map to the moduli space of some lattice-polarized K3 surfaces.关键词: The moduli of curves of genus six and K3 surfaces, Art...