D-local algebraic fundamental groups of germs of normal complex analytic singularities

2015/02/20 by Koji Ohno, Ohno, Koji
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.AG

paper · pdf · doi:10.48550/arxiv.1502.05766

arXiv admin note: substantial text overlap with arXiv:0710.3641

arxiv created 2015/02/20 · arxiv updated 2015/02/23

Abstract

In this paper, the notion of local algebraic fundamental groups of normal complex analytic singularities are generalized to certain profinite groups called D-local algebraic fundamental groups which turns out to be useful even for the study of usual local algebraic fundamental groups and the Lefshetz type theorem for D-local algebraic fundamental groups is proved under certain conditions. The theorem yields, for example, the finiteness of the local algebraic fundamental groups of a certain class of four dimensional singularities and will be useful for the classification of three dimensional purely log terminal singularities.

Citations

• The Euler Characteristic Formula for Logarithmic Minimal Degenerations of Surfaces with Kodaira Dimension Zero and its application to Calabi-Yau Threefolds with a pencil

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