53 citations · 130 across the 9 of their papers we have counts for
9 papers
On the finite generation of valuation semigroups on toric surfaces
Klaus Altmann, Christian Haase, Alex Küronya +2
We provide a combinatorial criterion for the finite generation of a valuation semigroup associated with an ample divisor on a smooth toric surface and a non-toric valuation of maxi…
Newton-Okounkov bodies sprouting on the valuative tree
C. Ciliberto, M. Farnik, A. Küronya +3
Given a smooth projective algebraic surface X, a point O in X and a big divisor D on X, we consider the set of all Newton-Okounkov bodies of D with respect to valuations of the fie…
Local positivity of linear series on surfaces
Alex Küronya, Victor Lozovanu
We study asymptotic invariants of linear series on surfaces with the help of Newton-Okounkov polygons. Our primary aim is to understand local positivity of line bundles in terms of…
Castelnuovo--Mumford Regularity and Log-canonical Thresholds
Alex Küronya, Norbert Pintye
We prove a sharp inequality relating the Castelnuovo--Mumford regularity of a coherent ideal sheaf to its log-canonical threshold.
Partial positivity: geometry and cohomology of q-ample line bundles
Daniel Greb, Alex Küronya
We give an overview of partial positivity conditions for line bundles, mostly from a cohomological point of view. Although the current work is to a large extent of expository natur…
Finite generation and geography of models
Anne-Sophie Kaloghiros, Alex Küronya, Vladimir Lazić
There are two main examples where a version of the Minimal Model Program can, at least conjecturally, be performed successfully: the first is the classical MMP associated to the ca…