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Gallarati studied contact of surfaces in $\mathbb{P}^3$, that is surfaces $V,W \subset \mathbb{P}^3$ such that $V.W = qD$ with $q$ an integer that is at least 2 and $D$ some curve. I would like to re …

My advisor told me the following: Let $\Sigma$ be a singular surface over $\mathbb{C}$ whose singularities are all ordinary quadratic, or more generally Duval singularities. Let $\epsilon: S \rightar …

I was told singular quartic algebraic surfaces in $\mathbb{P}^3_{\mathbb{C}}$ have been completely classified and their singularities have been described. Can anyone provide me with a resource where t …

Today i was talking with my advisor and she told me the following fact: Let $S$ be a singular surface in $\mathbb{P}^3_{\mathbb{C}}$ of degree $d$. Writing $\omega_\Sigma$ for the dualizing sheaf and …

Using Jason Starr's comment I was able (I think) to figure out the case of $\pi_1(X)^0$. For anyone who stumbles across this with the same question in mind I add a sketch of the proof in an answer. Fo …

Let $CH_0(X)^0$ denote the group of zero cycles of degree zero modulo rational equivalence. I am looking for a reference for the following fact: If $X$ and $Y$ are smooth and projective varieties ove …