8 problems

Let $\{(S_d,L_d)\}_{d\in\mathbb N}$ be very general polarized $K3$ surfaces with $L_d^2=2d-2$. Bastianelli–De Poi–Ein–Lazarsfeld–Ullery conjecture. … This predicts that the degrees…

Let $X_d$ be a quasismooth member of one of the eight deformation families numbered textnumero 1, textnumero 19, textnumero 28, textnumero 39, textnumero 49, textnumero 59, textnum…

Let $S_d$ be a very general polarized $K3$ surface with polarization $L_d$ such that $L_d^2=2d-2$, for each $d\in\mathbb N$. Unbounded irrationality conjecture. … The degree of irr…

A K3 surface is a smooth projective surface with trivial canonical bundle and $h^1(F,\mathcal O_F)=0$. K3 irrationality conjecture. The degree of irrationality of K3 surfaces $F$ i…

Bastianelli–de Poi–Ein–Lazarsfeld–Ullery conjecture.

Let $(S_d,L_d)$ be a polarized K3 surface of genus $d\geq 3$ such that … Write $\operatorname{irr}(S_d)$ for the degree of irrationality of $S_d$, and recall that the Konno invaria…

Let $X\subset \mathbb{P}^n$ be a generic hypersurface of degree $d\geq 2n-1$, and let $\mathrm{d}_r(X)$ denote its degree of irrationality. A dominant rational map is a rational ma…

Degree-of-irrationality conjecture. Except for finitely many genera, for every $1\leq k\leq g-1$ one has