\input zb-basic
\input zb-ioport
\iteman{io-port 06092107}
\itemau{Fr\"uhbis-Kr\"uger, Anne; Kadir, Shabnam}
\itemti{Zeta functions for families of Calabi-Yau $n$-folds with singularities.}
\itemso{Campillo, Antonio (ed.) et al., Zeta functions in algebra and geometry. Second international workshop, Universitat de les Illes Balears, Palma de Mallorca, Spain, May 3--7, 2010. Proceedings. Providence, RI: American Mathematical Society (AMS); Madrid: Real Sociedad Matem\'atica Espa\~nola (ISBN 978-0-8218-6900-0/pbk). Contemporary Mathematics 566, 21-41 (2012).}
\itemab
Relations beween the occurring singularity structure and the decomposition of the local zeta function in families of Calabi-Yau $n$-folds containing singular fibres are studied. Here the local zeta function for a smooth projective variety $X$ over $\mathbb{F}_p$ is defined s follows: $$ \varsigma(X|\mathbb{F}_p, t):=\exp(\sum\limits_{r\in \mathbb{N}}\# X(\mathbb{F}_{p^r})\frac{t^r}{r}). $$ Properties about the local zeta functions at good primes are listed. The singularities occurring in some $1$--dimensional and $2$--dimensional families (families of Fermat-type Calab-Yau $n$-folds) are analysed in detail. Examples of $2$--parameter families are especially studied. Here the singularity analysis provides correct predictions for the changes of degree in the decomposition of the zeta--function when passing to singular fibres.
\itemrv{Gerhard Pfister (Kaiserslautern)}
\itemcc{}
\itemut{zeta function; Calabi-Yau $n$-fold; singularity}
\itemli{doi:10.1090/conm/566/11213}
\end