4 problems

Complete saturation and reduction conjecture. Every body $K$ in $\mathbb{E}^d$ (respectively, in $\mathbb{H}^d$) admits a completely saturated packing and a completely reduced cove…

Let $d$ be a degree and let $\vec{e}=(e_1,\ldots,e_{d-1})$ be a $(d-1)$-tuple of scrollar invariants. A cover is primitive if it does not factor through a nontrivial proper subcove…

Let $\pi_2$ be the elliptic fibration constructed from a point of ${\mathcal M}'_{K,1}$, let $\sigma_0$ be its zero section, and let $\phi$ be the map associated with the correspon…

Let ${\mathcal L}$ be a rigid line configuration, and let $HK(n, {\mathcal L})$ be the associated Hirzebruch–Kummer covering of exponent $n$. Rigidity conjecture. If ${\mathcal L}$…