All Questions

I have a family of surfaces of general type $S$ with $q(S)=2$, and such that the Albanese map $$\alpha \colon S \longrightarrow A:=\mathrm{Alb}(S)$$ is generically finite of degree $n$. By a result of ...

I am interested in the following situation. If $S_1\cup_D S_2$ is a union of two irreducible smooth projective surfaces over $k=\overline{k}$(over $k=\mathbb{C}$ is enough, if it's relevant) glued ...

My question is related to this question, but I'm looking for something a bit more explicit. Let $S$ be a smooth surface over $\mathbb C$, fix a point $s\in S$ and take the blow up $\beta \colon S' \...

Are there known examples of smooth projective hypersurface in $\mathbb{P}^3$, say $X$ and an invertible sheaf $L$ on $X$ with $H^0(X,L)>0$ satisfying the following property: There exists an ...

NOTE: This is a followup to my question here. These are some questions concerning Mumford's "Lectures on curves on an algebraic surface". We concern ourselves with questions of the Picard variety $P$...

I am reading Ascher-Devleming-Liu's paper "Wall crossing for K-moduli spaces of plane curves" theorem 5.2 ADL19 and l have some confusions about the proof. Theorem 5.2 states that fixed a ...