R. Sanjeewa, T. Shaska
In previous work we determined automorphism groups of cyclic algebraic curves defined over fields of any odd characteristic. In this paper we determine parametric equations of families of curves for each automorphism group for such curves.
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We consider families of cyclic covers of the projective line, where we fix the covering group and the local monodromies and we vary the branch points. We prove that there are precisely twenty such families that give rise to a special subvariety in the moduli space of abelian varieties. Our proof uses techniques in mixed characteristics due to Dwork and Ogus.
We construct families of Calabi-Yau manifolds with dense set of complex multiplication fibers in an arbitrary dimension. We will also give explicite examples of complex multiplication fibers. For this construction we use families of curves with dense set of complex multiplication fibers. In addition, we give examples of such families for each genus less or equal 7 and we study the generic Hodge groups of families of cyclic covers of the projective line.
In this paper we describe six pencils of K3-surfaces which have large Picard-Number and contain precisely five singular fibers: four have A-D-E singularities and one is non-reduced. In particular we describe these surfaces as cyclic coverings of the K3-surfaces which Barth and the author described in a previous manuscript (Asian. J. of Math. Vol. 7, No. 4, 519-538, Dec. 2003). In many cases using this description and lattice-Theory we are able to compute the exact Picard-number and to describe explicitly the Picard-lattices.
Families of cyclic curve coverings with maximal monodromy
本文研究了具有最大单值性的循环曲线覆盖族，通过Hodge结构变分的G分解条件，证明了单值性最大性的判据，并探讨了双伽罗华覆盖和三伽罗华覆盖的测地性问题。
In this article we prove that the full automorphism group of a cyclic $p$-gonal pseudo-real Riemann surface of genus $g$ is either a semidirect product $C_{n}\ltimes C_{p}$ or a cyclic group, where $p$ is a prime $>2$ and $g>(p-1)^{2}$. We obtain necessary and sufficient conditions for the existence of a cyclic $p$-gonal pseudo-real Riemann surface with full\ automorphism group isomorphic to a given finite group. Finally we describe some families of cyclic $p$-gonal pseudo-real Riemann surfaces where the order of the full automorphism group is maximal and show that such families determine some…
Discriminant groups of wild cyclic quotient singularities
本文显式描述二维野循环商奇点的消解，证明奇素数下 p 的任意幂可为相交矩阵行列式，并支持野作用仅在原点分歧的猜想。
Calabi-Yau Varieties via Cyclic Covers, and Complex Hyperbolic Structures for their Moduli Spaces
研究通过循环覆盖得到的卡拉比 - 丘流形，其周期映射经复双曲球算术商分解，给出此类例子分类，证明单值群算术性及相关可公度关系，还得到德利涅 - 莫斯托理论中算术群的可公度关系。
Mass formula for non-ordinary curves in one dimensional families
本文研究正特征下射影直线循环覆盖一维族中非一般曲线的质量公式，通过tautological intersection theory和$a$-numbers证明两个方程，推广了Eichler--Deuring等人的结果并在超椭圆曲线等新情形下确定了公式。
Tautological families of cyclic covers of projective spaces
本文研究射影空间循环覆盖的tautological族存在性，给出存在条件并确定相关模空间的有理性，受超椭圆曲线模空间工作启发。
We propose a simple criterion to know if an abelian variety $A$ defined over a finite field $\mathbb{F}_q$ is cyclic, i.e., it has a cyclic group of rational points; this criterion is based on the endomorphism ring End$_{\mathbb{F}_q}(A)$. We also provide a criterion to know if an isogeny class is cyclic, i.e., all its varieties are cyclic; this criterion is based on the characteristic polynomial of the isogeny class. We find some asymptotic lower bounds on the fraction of cyclic $\mathbb{F}_q$-isogeny classes among certain families of them, when $q$ tends to infinity. Some of these bounds req…
Explicit supersingular cyclic curves
针对Li等人证明存在但未给出定义方程的Moonen分类下的超奇异循环曲线，研究通过带复乘曲线的模p约化将部分结果显式化，填补了该类曲线显式构造的空白。
Cohomological Kernels for Cyclic by Cyclic Semi-Direct Product Extensions
本文针对 Galois 闭包为循环群半直积的域扩张，利用 Positelski 的工具建立六项正合序列以刻画 Galois 上同调核，并涵盖相对 Brauer 群情形。
The aim of this note is to construct sequences of vector bundles with unbounded rank and discriminant on an arbitrary algebraic surface. This problem, on principally polarized abelian varieties with cyclic Neron-Severi group generated by the polarization, was considered by Nakashima in connection with the Douglas-Reinbacher-Yau conjecture on the Strong Bogomolov Inequality. In particular we show that on any surface, the Strong Bogomolov Inequality $SBI_l$ is false for all $l>4$.
Finite quotients of full surface braid groups and complex surfaces of general type: cyclic, dihedral, and extra-special quotients
研究亏格为\(g\)的紧致黎曼曲面上双股全辫群的有限循环、二面体和超特殊商群数量，在商映射特定条件下计算。并将代数结果用于构造一般型光滑曲面，得到两个三维族的极小曲面，其有相同双正则不变量和贝蒂数，但第一同调群挠部分不同。
Explicit bases for Riemann-Roch spaces on elliptic curves and their application in constructing various elliptic code families
本文提出了一种构造任意椭圆曲线分歧Riemann-Roch基的方法，并探讨其在密码学中的应用，特别是用于改进McEliece公钥密码系统。
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