70 citations · 417 across the 45 of their papers we have counts for
52 papers · 1 filter
Lifting negative curves from finite fields and Seshadri constants at ten points
Piotr Pokora, Tomasz Szemberg
We use finite-field calculations and mixed-characteristic deformation to construct nef divisors on very general complex blow-ups of the plane. A lifting and smoothing criterion con…
Demailly's Inequality for Finite Sets of Points in Positive Characteristic
Piotr Pokora, Tomasz Szemberg
Let be an algebraically closed field of characteristic , , and let be a finite nonempty set of distinct points with the defining ideal $I=I…
Companion varieties for root systems and Fermat arrangements
Roberta Di Gennaro, Giovanna Ilardi, Rosa Maria Miró-Roig +2
Unexpected hypersurfaces are a brand name for some special linear systems. They were introduced around 2017 and are a field of intensive study since then. They attracted a lot of a…
Conic-line arrangements in the complex projective plane
Piotr Pokora, Tomasz Szemberg
The main goal of this note is to begin a systematic study on conic-line arrangements in the complex projective plane. We show a de Bruijn-Erdős-type inequality and Hirzebruch-type…
On the number of vertices of Newton--Okounkov polygons
Joaquim Roé, Tomasz Szemberg
The Newton--Okounkov body of a big divisor D on a smooth surface is a numerical invariant in the form of a convex polygon. We study the geometric significance of the shape of Newto…
Negative curves on special rational surfaces
Marcin Dumnicki, Lucja Farnik, Krishna Hanumanthu +4
We study negative curves on surfaces obtained by blowing up special configurations of points in the complex projective palne. Our main results concern the following configurations:…