This paper considers the question of relative hyperbolicity of an Artin group with regard to the geometry of its associated Deligne complex. We prove that an Artin group is weakly hyperbolic relative to its finite (or spherical) type parabolic subgroups if and only if its Deligne complex is a Gromov hyperbolic space. For a 2-dimensional Artin group the Deligne complex is Gromov hyperbolic preci...

We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational.

We show that every supersingular K3 surface in characteristic 5 with Artin invariant ≤ 3 is unirational.

We classify stacky curves in characteristic p>0 with cyclic stabilizers of order p using higher ramification data. This approach replaces the local root stack structure a tame curve, similar to complex orbifold more sensitive called an Artin–Schreier stack, allowing us incorporate this data directly into stack. As application, we compute dimensions Riemann–Roch spaces for some examples positive...