arXiv subjects

Piotr Pokora

Publications and source records attributed to Piotr Pokora.

77 records · Page 5Linked to original sources

arXiv2014

Bounded Negativity and Arrangements of Lines

The Bounded Negativity Conjecture predicts that for any smooth complex surface $X$ there exists a lower bound for the selfintersection of reduced divisors on $X$. This conjecture is open. It is also not known if the existence of such a lower bound is invariant in the birational equivalence class of $X$. In the present note we introduce certain constants $H(X)$ which measure in effect the variance of the lower bounds in the birational equivalence class of $X$. We focus on rational surfaces and relate the value of $H({\mathbb P}^2)$ to certain line arrangements. Our main result is Theorem 3.3 and the main open challenge is Problem 3.10.

math.AG↗

arXiv2014

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↗

arXiv2014

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.

math.AG↗

arXiv2013

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.

math.RA↗

arXiv2013

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↗