53 citations · 64 across the 18 of their papers we have counts for
18 papers
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…
A Pascal-type construction of the Segre cubic and the Cremona--Richmond configuration
Piotr Pokora, Tomasz Szemberg
We present a Pascal-type residual construction in P^4. Starting from two quadruples of hyperplanes whose four diagonal intersection planes lie in a hyperplane, we show that the twe…
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…
Waldschmidt constants of symmetric sets of points in
Sebastian Calvo, Jack Huizenga, Tomasz Szemberg
Configurations of points defined by complex reflection groups have attracted a lot of attention recently in several directions of research, e.g., the containment problem between or…
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…
Line arrangements with many triple points
Lukas Kühne, Tomasz Szemberg, Halszka Tutaj-Gasińska
In this paper, we construct an infinite series of line arrangements in characteristic two, each featuring only triple intersection points. This finding challenges the existing conj…
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 …
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…
Line arrangements with the maximal number of triple points
Marcin Dumnicki, Lucja Farnik, Agata Glowka +5
The purpose of this note is to study configurations of lines in projective planes over arbitrary fields having the maximal number of intersection points where three lines meet. We…
Negative curves on algebraic surfaces
Th. Bauer, B. Harbourne, A. L. Knutsen +4
We study curves of negative self-intersection on algebraic surfaces. We obtain results for smooth complex projective surfaces X on the number of reduced, irreducible curves C of ne…