All Questions

Does there exists a cubic or quartic $3$-fold $X\subset\mathbb{P}^4$ such that $Sing(X)$ is a smooth curve $C$ of genus $g(C)\geq 2$ and $X$ has $A_1$-singularities along $C$?

Let $p$ be a prime number and let $\bar{\mathbb F}_p$ be an algebraic closure of $\mathbb F_p$. Let $C$ be an irreducible singular projective curve over $\bar{\mathbb F}_p$. Let $P$ be a singularity ...

A proof from Janos Kollar's Lectures on Resolution of Singularities Kollar (p 37) works as follows: Theorem 1.58 (M. Noether, 1871). Let $k$ be an algebraically closed field and $C \subset \...

I would like to better understand a certain compactification of the Jacobian variety of a singular algebraic plane curve as described in Cook's Ph.D. 1993 thesis Local and Global Aspects of the Module ...