arXiv subjects

Stiofáin Fordham

Publications and source records attributed to Stiofáin Fordham.

2 recordsLinked to original sources

arXiv2018

On the level of a Calabi-Yau hypersurface

Boix-De Stefani-Vanzo defined the notion of level for a smooth projective hypersurface over a finite field in terms of the stabilisation of a chain of ideals previously considered by Àlvarez-Montaner-Blickle-Lyubeznik, and showed that in the case of an elliptic curve the level is 1 if and only if it is ordinary and 2 otherwise. Here we extend their theorem to the case of Calabi-Yau hypersurfaces by relating their level to the $F$-jumping exponents of Blickle-Mustaţă-Smith and the Hartshorne-Speiser-Lyubeznik numbers of Mustaţă-Zhang.

math.AG↗

arXiv2018

Differential operators and hyperelliptic curves over finite fields

Boix, De Stefani and Vanzo have characterized ordinary/supersingular elliptic curves over $\mathbb{F}_p$ in terms of the level of the defining cubic homogenous polynomial. We extend their study to arbitrary genus, in particular we prove that every ordinary hyperelliptic curve $\mathcal{C}$ of genus $g\geq 2$ has level $2$. We provide a good number of examples and raise a conjecture.

math.NT↗