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Let $\pi\colon X\to Y$ be a proper morphism of smooth complex algebraic varieties with $\dim X = 2n$ and general fibers of dimension $<n$. Assume that $F := \pi^{-1}(p)$ is a an irreducible and reduce …

Let $f\colon X\to \mathbb P^1$ be a proper morphism of smooth complex algebraic varieties and let $p\in\mathbb P^1$. Are there a complex disk $\Delta\subseteq\mathbb P^1$ and a Zariski open subset $U\ …

What is the maximum number of concurrent bitangents, i.e. all intersecting at the same point, of a smooth complex projective quartic curve? Can the number of concurrent bitangents be six?

Let $\mathbb K$ be a field of characteristic $p>0$. Let $f\in\mathbb K[x_1,\dots,x_n]$ be a multivariate polynomial and let $q\in\mathbb K^n$. Is there a computational method to determine the multipli …

Let $P\subseteq\mathbb R^n$ be a centrally symmetric lattice polytope whose only interior lattice point is the zero vector. Is it true that $P$ is equivalent (up to ${\rm GL}(n,\mathbb Z)$ + lattice t …