39 citations · 156 across the 32 of their papers we have counts for
42 papers
Dihedral reflections and an infinite series of irrational Seshadri constants
Grzegorz Malara, Łukasz Merta, Justyna Szpond +1
Laface and Ugaglia recently constructed an irrational one-point Seshadri constant on the blow-up of at nine very general points by combining a dihedral orbit on $\ma…
Artin-Schreier geproci configurations in projective spaces of arbitrary dimension
Luca Chiantini, Lucja Farnik, Giuseppe Favacchio +4
We construct finite geproci sets in every projective dimension and in every positive characteristic by introducing -Artin-Schreier configurations. In ,…
Enumerative geometry of skew lines in with a given associated finite group
Luca Chiantini, Łucja Farnik, Giuseppe Favacchio +4
For any finite set of 3 or more skew lines in over an algebraically closed field of arbitrary characteristic, there is a ca…
From a Pascal construction to the Burkhardt quartic
Tomasz Szemberg, Justyna Szpond
We continue the study of Pascal-type residual constructions in projective four-space. Starting from two -tuples of hyperplanes in such that the diagonal inters…
Weddle schemes
Luca Chiantini, Łucja Farnik, Giuseppe Favacchio +4
The classical Weddle surface is the locus of vertices of quadric cones through six points in in linear general position. Equivalently, it is the closure of the locus…
Intersection of curves in projective 4 space
Luca Chiantini, Łucja Farnik, Giuseppe Favacchio +4
Given two distinct reduced, irreducible curves of given degrees, contained in projective space but whose union is not contained in a hyperplane, what is the largest number of point…
Postulation of lines in P3 revisited
Marcin Dumnicki, Mikolaj Le Van, Grzegorz Malara +3
The purpose of the present note is to provide a new proof ot the well-known result due to Hartshorne and Hirschowitz to the effect that general lines in projective spaces have good…
Finite sets of points in with special projection properties
Luca Chiantini, Łucja Farnik, Giuseppe Favacchio +4
In this note we introduce the notion of -geprofi sets and study their basic properties. These are sets of points in whose projection from a general point…
Geproci sets on skew lines in with two transversals
Luca Chiantini, Pietro De Poi, Lucja Farnik +6
The purpose of this work is to pursue classification of geproci sets. Specifically we classify -geproci sets which consist of points on each of skew lines, assumin…
Combinatorics of skew lines in with an application to algebraic geometry
Luca Chiantini, Łucja Farnik, Giuseppe Favacchio +4
This article introduces a previously unrecognized combinatorial structure underlying configurations of skew lines in , and reveals its deep and surprising connection…
On the classification of certain geproci sets
Luca Chiantini, Lucja Farnik, Giuseppe Favacchio +4
In this short note we develop new methods toward the ultimate goal of classifying geproci sets in . We apply these methods to show that among sets of points distr…
Sextactic points on the Fermat cubic curve and arrangements of conics
Tomasz Szemberg, Justyna Szpond
The purpose of this note is to report, in narrative rather than rigorous style, about the nice geometry of -division points on the Fermat cubic and various conics naturally…
Configurations of points in projective space and their projections
Luca Chiantini, Łucja Farnik, Giuseppe Favacchio +4
We call a set of points an -geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point …
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…
Unexpected properties of the Klein configuration of points in
Piotr Pokora, Tomasz Szemberg, Justyna Szpond
Felix Klein in course of his study of the regular icosahedron and its symmetries encountered a highly symmetric configuration of points in . This configuration…
Fermat-type arrangements
Justyna Szpond
The purpose of this work is to collect in one place available information on line arrangements known in the literature as braid, monomial, Ceva or Fermat arrangement. They have bee…
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:…
A matrixwise approach to unexpected hypersurfaces
Marcin Dumnicki, Lucja Farnik, Brian Harbourne +3
The aim of this note is to give a generalization of some results concerning unexpected hypersurfaces. Unexpected hypersurfaces occur when the actual dimension of the space of forms…
Unexpected hypersurfaces with multiple fat points
Justyna Szpond
Starting with the ground-breaking work of Cook II, Harbourne, Migliore and Nagel, there has been a lot of interest in unexpected hypersurfaces. In the last couple of months a consi…
Unexpected curves and Togliatti-type surfaces
Justyna Szpond
The purpose of this note is to establish a direct link between the theory of unexpected hypersurfaces and varieties with defective osculating behavior. We identify unexpected plane…
Quartic unexpected curves and surfaces
Thomas Bauer, Grzegorz Malara, Tomasz Szemberg +1
Our research is motivated by recent work of Cook II, Harbourne, Migliore, and Nagel on configurations of points in the projective plane with properties that are unexpected from the…
Lower bounds for Waldschmidt constants of generic lines in and a Chudnovsky-type theorem
Marcin Dumnicki, Mohammad Zaman Fashami, Justyna Szpond +1
The Waldschmidt constant $\alphahat(I)$ of a radical ideal in the coordinate ring of $\PP^N$ measures (asymptotically) the degree of a hypersurface passing through the set defi…
Local effectivity in projective spaces
Marcin Dumnicki, Tomasz Szemberg, Justyna Szpond
In this note we introduce a Waldschmidt decomposition of divisors which might be viewed as a generalization of Zariski decomposition based on the effectivity rather than the nefnes…
The containment problem and a rational simplicial arrangement
G. Malara, J. Szpond
Since Dumnicki, Szemberg and Tutaj-Gasińska 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 conta…