70 citations · 417 across the 45 of their papers we have counts for
54 papers
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:…