Zeta-Functions for Families of Calabi--Yau n-folds with Singularities

Anne Frühbis-Krüger, Shabnam Kadir

Research output: Chapter in Book/Report/Conference proceedingChapter


We consider families of Calabi-Yau n-folds containing singular fibres and study relations between the occurring singularity structure and the decomposition of the local Weil zeta-function. For 1-parameter families, this provides new insights into the combinatorial structure of the strong equivalence classes arising in the Candelas - de la Ossa - Rodrigues-Villegas approach for computing the zeta-function. This can also be extended to families with more parameters as is explored in several examples, where the singularity analysis provides correct predictions for the changes of degree in the decomposition of the zeta-function when passing to singular fibres. These observations provide first evidence in higher dimensions for Lauder's conjectured analogue of the Clemens-Schmid exact sequence.
Original languageEnglish
Title of host publication Zeta functions for families of Calabi–Yau n -folds with singularities
EditorsAntonio Campillo, Gabriel Cardona, Alejandro Melle-Hernandez, Wim Veys, Wilson A. Zuniga-Galindo
PublisherAmerican Mathematical Society
ISBN (Electronic)978-0-8218-8776-9
ISBN (Print)978-0-8218-6900-0
Publication statusPublished - 2 Feb 2012

Publication series

NameContemporary Mathematics
PublisherAmerican Mathematical Society


  • math.AG


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