A counterexample to the containment $I^{(3)}\subset I^2$ over the reals
The purpose of this note is to give counterexamples to the containment $I^{(3)}\subset I^2$ over the real numbers.
math.AG↗
arXiv subjects
Piotr Pokora
Publications and source records attributed to Piotr Pokora.
Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone
The purpose of this note is to study the number of elements in Minkowski bases on algebraic surfaces with rational polyhedral pseudo-effective cone.
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Rank Function Equations and their solution sets
We examine so-called rank function equations and their solutions consisting of non-nilpotent matrices. Secondly, we present some geometrical properties of the set of solutions to certain rank function equations in the nilpotent case.
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Points fattening on P^1 x P^1 and symbolic powers of bi-homogeneous ideals
We study symbolic powers of bi-homogeneous ideals of points in the Cartesian product of two projective lines and extend to this setting results on the effect of points fattening obtained by Bocci, Chiantini and Dumnicki, Szemberg, Tutaj-Gasińska. We prove a Chudnovsky-type theorem for bi-homogeneous ideals and apply it to classification of configurations of points with minimal or no fattening effect. We hope that the ideas developed in this project will find further algebraic and geometric applications e.g. to study similar problems on arbitrary surfaces.
math.AG↗