Grzegorz Malara

A counterexample to the containment I(3) ⊂ I2 over the reals

The purpose of this note is to give counterexamples to the con- tainment I (3) I 2 over the real numbers.

Initial sequences and Waldschmidt constants of planar point configurations

The purpose of this work is to extend the classification of planar point configurations with low Waldschmidt constants for all values less than

Fermat-type configurations of lines in P3 and the containment problem

5/2

Points fattening on P1×P1 and symbolic powers of bi-homogeneous ideals

. As a consequence we prove a conjecture of Dumnicki, Szemberg and Tutaj-Gasinska concerning initial sequences with low first differences.

On the containment hierarchy for simplicial ideals

Abstract The purpose of this note is to show a new series of examples of homogeneous ideals I in K [ x , y , z , w ] for which the containment I ( 3 ) ⊂ I 2 fails. These ideals are supported on certain arrangements of lines in P 3 , which resemble Fermat configurations of points in P 2 , see [14] . All examples exhibiting the failure of the containment I ( 3 ) ⊆ I 2 constructed so far have been supported on points or cones over configurations of points. Apart from providing new counterexamples, these ideals seem quite interesting on their own.