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Zeta function of Hypersurfaces with ADE singularities in $\mathbb{P}^{3}$
Abstract
Stetson and Baranovsky provided an algorithm with Mathematica to compute the zeta function of projective hypersurface over $\mathbb{F}_{p}$ with isolated ordinary double points. In this thesis, I extend this algorithm to hypersurfaces with ADE singularities over $\mathbb{P}^{3}$. In the process of doing so, I characterize the Jacobian ideal as a zero set of differential operators.