Let M g be the moduli space of curves of genus g. If A g is the space of principally polarized d-dimensional abelian varieties then there is a natural morphism j:M g →A g defined by sending a curve to its jacobian. It is a classical problem to give a set of equations for the ...
We begin with an exposition of some of Dennis Johnson's work on the Torelli groups. We then show how these results imply that the Picard group of the moduli space of curves of genus g ≥ 3witha level-l structure is finitely generated. A classification of all "natural " normal functions...
The Moduli Space of Curves 来自 Semantic Scholar 喜欢 0 阅读量: 70 作者: R Dijkgraaf 摘要: 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 ...
Planofthispaper:Inthefollowingsection,werevisebasicfactson weightedpointedcurvesofgenuszero,theirmodulispaceM A ,andthecom- binatorialstratificationofM A .InSection3,weconsiderrestrictionsof forgetfulmorphismstothestrataofM A andstudytheirfibers.Wecalculate therelativehomologyofthestratainductivelybyusingfo...
(recall that if p : ˜X→X is the blow up of a smooth threefold along a smooth curve with exceptional divisor E then E.p∗C=0 for every curve C⊂X, see for instance [6] ,Lemma 1). QUANTUM COHOMOLOGY OF MODULI OF GENUS ZERO CURVES 7 ...
In this note, we prove that the Q-Picard group of the moduli space of n-pointed stable curves of genus g over an algebraically closed field is generated by the tautological classes. We also prove that the cycle map to the 2nd etale cohomology group is bi
We present a structure theorem for the moduli spaceR7of Prym curves of genus 7 as a projective bundle over the moduli space of 7-nodal rational curves. The... G Farkas,A Verra - 《Advances in Mathematics》 被引量: 3发表: 2016年 Prym varieties and moduli of polarized Nikulin surfaces We...
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...
Moduli of vector bundlesLet $C$ be an algebraic curve of genus $g\\ge2$. A coherent system on $C$ consists of a pair $(E,V)$, where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of the space of sections...
Pandharipande-Pixton have used the geometry of the moduli space of stable quotients to produce relations between tautological Chow classes on the moduli space M_g of smooth genus g curves. We study a natural extension of their methods to the boundary and more generally to Hassett's moduli ...