1,291 research outputs found
On the nearly free simplicial line arrangements with up to 27 lines
In the present note we provide a complete classification of
nearly free (and not free simultaneously) simplicial arrangements of d ⩽ 27
lines
The containment problem and a rational simplicial arrangement
Since Dumnicki, Szemberg and Tutaj-Gasi\'nska gave in 2013 in [9] the first
example of a set of points in the complex projective plane such that for its
homogeneous ideal I the containment of the third symbolic power in the second
ordinary power fails, there has been considerable interest in searching for
further examples with this property and investigating into the nature of such
examples. Many examples, defined over various fields, have been found but so
far there has been essentially just one example found of 19 points defined over
the rationals, see [16, Theorem A, Problem 1]. In [12, Problem 5.1] the authors
asked if there are other rational examples. This has motivated our research.
The purpose of this note is to flag the existence of a new example of a set of
49 rational points with the same non-containment property for powers of its
homogeneous ideal. Here we establish the existence and justify it
computationally. A more conceptual proof, based on Seceleanu's criterion [20]
will be published elsewhere [17]
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