70 citations · 116 across the 14 of their papers we have counts for
15 papers · 1 filter
On submaximal curves in fake projective planes
Piotr Pokora, Halszka Tutaj-Gasinska
The main purpose of the note is to exclude the existence of certain submaximal curves in fake projective planes. This will lead to lower bounds on multipoint Seshadri constants of…
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…
Veneroni maps
M. Dumnicki, L. Farnik, B. Harbourne +2
Veneroni maps are a class of birational transformations of projective spaces. This class contains the classical Cremona transformation of the plane, the cubo-cubic transformation o…
Containment problem and combinatorics
Łucja Farnik, Jakub Kabat, Magdalena Lampa-Baczyńska +1
In this note we consider two configurations of twelve lines with nineteen triple points (i.e., points where three lines meet). Both of them have the same combinatorial features. In…
A containment result in and the Chudnovsky conjecture
Marcin Dumnicki, Halszka Tutaj-Gasinska
In the paper we prove the containment , for a radical ideal of general points in , where . As a corollary we get tha…
Restrictions on Seshadri constants on surfaces
Lucja Farnik, Tomasz Szemberg, Justyna Szpond +1
Starting with the pioneering work of Ein and Lazarsfeld restrictions on values of Seshadri constants on algebraic surfaces have been studied by many authors. In the present note we…
Asymptotic Hilbert Polynomial and a bound for Waldschmidt constants
Marcin Dumnicki, Lucja Farnik, Halszka Tutaj-Gasinska
In the paper we give an upper bound for the Waldschmidt constants of the wide class of ideals. This generalizes the result obtained by Dumnicki, Harbourne, Szemberg and Tutaj-Gasin…
Symbolic powers of planar point configurations II
Marcin Dumnicki, Tomasz Szemberg, Halszka Tutaj-Gasinska
We study initial sequences of various configurations of planar points. We answer several questions asked in our previous paper (Symbolic powers of planar point configurations), and…
On the Sylvester-Gallai theorem for conics
Adam Czaplinski, Marcin Dumnicki, Lucja Farnik +6
In the present note we give a new proof of a result due to Wiseman and Wilson which establishes an analogue of the Sylvester-Gallai theorem valid for curves of degree two. The main…
Asymptotic Hilbert Polynomial and limiting shapes
Marcin Dumnicki, Justyna Szpond, Halszka Tutaj-Gasinska
The main aim of this paper is to provide a method which allows finding limiting shapes of symbolic generic initial systems of higher-dimensional subvarieties of P^n. M. Mustata and…
Symbolic generic initial systems of star configurations
Marcin Dumnicki, Tomasz Szemberg, Justyna Szpond +1
The purpose of this note is to describe limiting shapes (as introduced by Mayes) of symbolic generic initial systems of star configurations in projective spaces over a field of cha…
A vanishing theorem and symbolic powers of planar point ideals
Marcin Dumnicki, Tomasz Szemberg, Halszka Tutaj-Gasinska
The purpose of this note is twofold. We present first a vanishing theorem for families of linear series with base ideal being a fat points ideal. We apply then this result in order…
Counterexamples to the containment
Marcin Dumnicki, Tomasz Szemberg, Halszka Tutaj-Gasinska
We show that in general the third symbolic power of a radical ideal of points in the complex projective plane is not contained in the second usual power of that ideal. This answers…
Symbolic powers of planar point configurations
Marcin Dumnicki, Tomasz Szemberg, Halszka Tutaj-Gasinska
We study initial degrees of symbolic powers of ideals of arbitrary finite sets of points in the projective plane over an algebraically closed field of characteristic zero. We show,…