The Intersection of Two Fermat Hypersurfaces in P^3 via Computation of Quotient Curves

Details The Intersection of Two Fermat Hypersurfaces in P^3 via Computation of Quotient Curves The Intersection of Two Fermat Hypersurfaces in P^3 via Computation of Quotient Curves

2009-11-20

arxiv.org/abs/0911.4025v2

Mathematics

Algebraic Geometry

Scientific paper

We study the intersection of two particular Fermat hypersurfaces in $\mathbb{P}^3$ over a finite field. Using the Kani-Rosen decomposition we study arithmetic properties of this curve in terms of its quotients. Explicit computation of the quotients is done using a Gr\"obner basis algorithm. We also study the $p$-rank, zeta function, and number of rational points, of the modulo $p$ reduction of the curve. We show that the Jacobian of the genus 2 quotient is $(4,4)$-split.

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