Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userModuli of certain wild covers of curves
89
0
0.0
(
0
)
Authors
Jianru Zhang
Ask ChatGPT about the research
No Arabic abstract
A fine moduli space is constructed, for cyclic-by-$mathsf{p}$ covers of an affine curve over an algebraically closed field $k$ of characteristic $mathsf{p}>0$. An intersection of finitely many fine moduli spaces for cyclic-by-$mathsf{p}$ covers of affine curves gives a moduli space for $mathsf{p}$-by-$mathsf{p}$ covers of an affine curve. A local moduli space is also constructed, for cyclic-by-$mathsf{p}$ covers of $Spec(k((x)))$, which is the same as the global moduli space for cyclic-by-$mathsf{p}$ covers of $mathbb{P}^1-{0}$ tamely ramified over $infty$ with the same Galois group. Then it is shown that a restriction morphism is finite with degrees on connected components $mathsf{p}$ powers: There are finitely many deleted points of an affine curve from its smooth completion. A cyclic-by-$mathsf{p}$ cover of an affine curve gives a product of local covers with the same Galois group of the punctured infinitesimal neighbourhoods of the deleted points. So there is a restriction morphism from the global moduli space to a product of local moduli spaces.
rate research
Read More
It is well known that the Prym variety of an etale cyclic covering of a hyperelliptic curve is isogenous to the product of two Jacobians. Moreover, if the degree of the covering is odd or congruent to 2 mod 4, then the canonical isogeny is an isomorphism. We compute the degree of this isogeny in the remaining cases and show that only in the case of coverings of degree 4 it is an isomorphism.
We compute the number of moduli of all irreducible components of the moduli space of smooth curves on Enriques surfaces. In most cases, the moduli maps to the moduli space of Prym curves are generically injective or dominant. Exceptional behaviour is related to existence of Enriques--Fano threefolds and to curves with nodal Prym-canonical model.
This survey article discusses some results on the structure of families f:V-->U of n-dimensional manifolds over quasi-projective curves U, with semistable reduction over a compactification Y of U. We improve the Arakelov inequality for the direct images of powers of the dualizing sheaf. For families of Abelian varieties we recall the characterization of Shimura curves by Arakelov equalities. For families of curves we recall the characterization of Teichmueller curves in terms of the existence of certain sub variation of Hodge structures. We sketch the proof that the moduli scheme of curves of genus g>1 can not contain compact Shimura curves, and that it only contains a non-compact Shimura curve for g=3.
This article accompanies my lecture at the 2015 AMS summer institute in algebraic geometry in Salt Lake City. I survey the recent advances in the study of tautological classes on the moduli spaces of curves. After discussing the Faber-Zagier relations on the moduli spaces of nonsingular curves and the kappa rings of the moduli spaces of curves of compact type, I present Pixtons proposal for a complete calculus of tautological classes on the moduli spaces of stable curves. Several open questions are discussed. An effort has been made to condense a great deal of mathematics into as few pages as possible with the hope that the reader will follow through to the end.
We introduce the moduli space of hybrid curves as the hybrid compactification of the moduli space of curves thereby refining the one obtained by Deligne and Mumford. As the main theorem of this paper we then show that the universal family of canonically measured hybrid curves over this moduli space varies continuously. On the way to achieve this, we present constructions and results which we hope could be of independent interest. In particular, we introduce higher rank variants of hybrid spaces which refine and combine both the ones considered by Berkovich, Boucksom and Jonsson, and metrized complexes of varieties studied by Baker and the first named author. Furthermore, we introduce canonical measures on hybrid curves which simultaneously generalize the Arakelov-Bergman measure on Riemann surfaces, Zhang measure on metric graphs, and Arakelov-Zhang measure on metrized curve complexes. This paper is part of our attempt to understand the precise link between the non-Archimedean Zhang measure and variations of Arakelov-Bergman measures in families of Riemann surfaces, answering a question which has been open since the pioneering work of Zhang on admissible pairing in the nineties.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
