70 citations · 417 across the 45 of their papers we have counts for
8 papers · 1 filter
Very general monomial valuations of and a Nagata type conjecture
Marcin Dumnicki, Brian Harbourne, Alex Küronya +2
It is well known that multi-point Seshadri constants for a small number of points in the projective plane are submaximal. It is predicted by the Nagata conjecture that their va…
The effect of points fattening on Hirzebruch surfaces
Sandra Di Rocco, Anders Lundman, Tomasz Szemberg
The purpose of this note is to study initial sequences of zero-dimensional subschemes of Hirzebruch surfaces and classify subschemes whose initial sequence has the minimal possible…
The effect of points fattening in dimension three
Thomas Bauer, Tomasz Szemberg
There has been increased recent interest in understanding the relationship between the symbolic powers of an ideal and the geometric properties of the corresponding variety. While…
Vanishing sequences and Okounkov bodies
Sébastien Boucksom, Alex Küronya, Catriona Maclean +1
We define and study the vanishing sequence along a real valuation of sections of a line bundle on a projective variety. Building on previous work of the first author with Huayi Che…
Points fattening on P^1 x P^1 and symbolic powers of bi-homogeneous ideals
Magdalena Baczyńska, Marcin Dumnicki, Agata Habura +5
We study symbolic powers of bi-homogeneous ideals of points in the Cartesian product of two projective lines and extend to this setting results on the effect of points fattening ob…
Seshadri constants via Okounkov functions and the Segre-Harbourne-Gimigliano-Hirschowitz Conjecture
Marcin Dumnicki, Alex Küronya, Catriona Maclean +1
In this note we relate the SHGH Conjecture to the rationality of one-point Seshadri constants on blow ups of the projective plane, and explain how rationality of Seshadri constants…