关于相关Picard-Fuchs系统的混合扭曲结构和单调性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-08-16 DOI:10.4310/CNTP.2022.v16.n3.a2

Andreas Malmendier, Michael T. Schultz

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引用次数: 0

摘要

.我们使用Doran和Malmendier的混合扭曲构造，得到了Picard秩ρ≥16的K3曲面的多参数族。在确定其一般成员上的特定雅可比椭圆振动后，我们确定了该族的晶格极化和Picard-Fuchs系统。我们构造了一系列的限制，这些限制导致两个基本晶格的极化扩展。我们证明了限制族的Picard-Fuchs算子与已知的共振超几何系统是一致的。其次，对于变形Fermat超曲面的单参数镜像族，我们证明了混合扭曲结构产生了一个非共振GKZ系统，对于该系统，存在绝对收敛Mellin-Barnes积分形式的解的基，我们显式计算了其单调性。

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On the mixed-twist construction and monodromy of associated Picard–Fuchs systems

. We use the mixed-twist construction of Doran and Malmendier to obtain a multi-parameter family of K3 surfaces of Picard rank ρ ≥ 16. Upon identifying a particular Jacobian elliptic ﬁbration on its general member, we determine the lattice polarization and the Picard-Fuchs system for the family. We construct a sequence of restrictions that lead to extensions of the polarization by two-elementary lattices. We show that the Picard-Fuchs operators for the restricted families coincide with known resonant hypergeometric systems. Second, for the one-parameter mirror families of deformed Fermat hypersurfaces we show that the mixed-twist construction produces a non-resonant GKZ system for which a basis of solutions in the form of absolutely convergent Mellin-Barnes integrals exists whose monodromy we compute explicitly.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.