arXiv 0806.33112008-06math.AG

Zariski-van Kampen method and transcendental lattices of certain singular K3 surfaces

Ken-ichiro Arima, Ichiro Shimada

备注：: 24 pages, typos are corrected, references are updated, a new figure is added

英文摘要：

We present a method of Zariski-van Kampen type for the calculation of the transcendental lattice of a complex projective surface. As an application, we calculate the transcendental lattices of complex singular K3 surfaces associated with an arithmetic Zariski pair of maximizing sextics of type $A_{10}+A_{9}$ that are defined over a real quadratic field and are conjugate to each other over the field of rational numbers.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Generalized Zariski-van Kampen theorem and its application to Grassmannian dual varieties

We formulate and prove a generalization of Zariski-van Kampen theorem on the topological fundamental groups of smooth complex algebraic varieties. As an application, we prove a hyperplane section theorem of Lefschetz-Zariski-van Kampen type for the fundamental groups of the complements to the Grassmannian dual varieties.

2009-06-05math.AG

Zariski-van Kampen theorems for singular varieties --- an approach via the relative monodromy variation

The classical Zariski-van Kampen theorem gives a presentation of the fundamental group of the complement of a complex algebraic curve in $\mathbb{P}^2$. The first generalization of this theorem to singular (quasi-projective) varieties was given by the first author. In both cases, the relations are generated by the standard monodromy variation operators associated with the special members of a generic pencil of hyperplane sections. In the present paper, we give a new generalization in which the relations are generated by the relative monodromy variation operators introduced by D. Chéniot and th…

2016-09-06math.AG

Homotopical variations and high-dimensional Zariski-van Kampen theorems

In 1933, van Kampen described the fundamental groups of the complements of plane complex projective algebraic curves. Recently, Chéniot-Libgober proved an analogue of this result for higher homotopy groups of the complements of complex projective hypersurfaces with isolated singularities. Their description is in terms of some "homotopical variation operators". We generalize here the notion of "homotopical variation" to (singular) quasi-projective varieties. This is a first step for further generalizations of van Kampen's theorem. A conjecture, with a first approach, is stated in the special ca…

2002-04-13math.AGmath.ATmath.CV

Zariski-van Kampen theorem for higher homotopy groups

This paper gives an extension of the classical Zariski-van Kampen theorem describing the fundamental groups of the complements of plane singular curves by generators and relations. It provides a procedure for computation of the first non-trivial higher homotopy groups of the complements of singular projective hypersurfaces in terms of the homotopy variation operators introduced here.

2003-03-01math.AGmath.ATmath.CV

The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

2005-04-08math.AGmath.CV

Restricted volumes and divisorial Zariski decompositions

We give a relation between the existence of a Zariski decomposition and the behavior of the restricted volume of a big divisor on a smooth (complex) projective variety. Moreover, we give an analytic description of the restricted volume in the line of Boucksom's work. It enables us to define the restricted volume of a transcendental class on a compact Kähler manifold in natural way. The relation can be extended to a transcendental class.

2013-01-16math.AGmath.CV

更多相关论文收起更多论文

The fundamental group of a generalized trigonal curve

We develop a modification of the Zariski--van Kampen approach for the computation of the fundamental group of a trigonal curve with improper fibers. As an application, we list the deformation families and compute the fundamental groups of all irreducible maximizing simple sextics with a type $\bold D$ singular point.

2009-10-01math.AG

具有相同极大环面的单代数群、弱可公度Zariski稠密子群与良好约化

Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction

本研究提出了基于特殊极大环面存在性的绝对殆单代数群良好约化新判定条件，推导了有限性猜想与群亏格有限性的关联，发现纯超越扩张消亏格现象，研究了Zariski稠密子群特征值刚性，并分析了F₄型单代数群的相关问题。

2023-12-14math.AGmath.GRmath.NT

关于X-态簇的研究

On the variety of X-states

本文引入n量子比特X-态概念，通过Zariski闭包构造复代数簇并研究局部对称群作用，证明其不变有理函数域为纯超越扩张，超越次数为$2^{2n-1}-n-1$。

2024-02-27math-phmath.AGmath.MP