10 citations · 32 across the 14 of their papers we have counts for
15 papers
The Nash problem for torus actions of complexity one
David Bourqui, Kevin Langlois, Hussein Mourtada
We solve the equivariant generalized Nash problem for any non-rational normal variety with torus action of complexity one. Namely, we give an explicit combinatorial description of…
Reductive quotients of klt singularities
Lukas Braun, Daniel Greb, Kevin Langlois +1
We prove that the quotient of a klt type singularity by a reductive group is of klt type. In particular, given a klt variety endowed with the action of a reductive group an…
On intersection cohomology with torus action of complexity one, II
Marta Agustin Vicente, Narasimha Chary Bonala, Kevin Langlois
We show that the components, appearing in the decomposition theorem for contraction maps of torus actions of complexity one, are intersection cohomology complexes of even codimensi…
Decomposition theorem and torus actions of complexity one
Marta Agustin Vicente, Kevin Langlois
We algorithmically compute the intersection cohomology Betti numbers of any complete normal algebraic variety with a torus action of complexity one.
Horizontal Ga-actions on affine T-varieties of complexity one
Kevin Langlois
We classify the -actions on normal affine varieties defined over any field that are horizontal with respect to a torus action of complexity one. This generalizes pr…
Models of affine curves and Ga-actions
Kevin Langlois
Using the approach of Barkatou and El Kaoui, we classify certain affine curves over discrete valuation rings having a free additive group action. Our classification generalizes res…
Horospherical stacks
Ariyan Javanpeykar, Kevin Langlois, Ronan Terpereau
We prove structure theorems for algebraic stacks with a reductive group action and a dense open substack isomorphic to a horospherical homogeneous space, and thereby obtain new exa…
On the classification of normal G-varieties with spherical orbits
Kevin Langlois
In this article, we investigate the geometry of reductive group actions on algebraic varieties. Given a connected reductive group , we elaborate on a geometric and combinatorial…
The Cox ring of a complexity-one horospherical variety
Kevin Langlois, Ronan Terpereau
Cox rings are intrinsic objects naturally generalizing homogeneous coordinate rings of projective spaces. A complexity-one horospherical variety is a normal variety equipped with a…
Stringy invariants for horospherical varieties of complexity one
Kevin Langlois, Clélia Pech, Michel Raibaut
In this paper we determine the stringy motivic volume of log terminal horospherical -varieties of complexity one, where is a connected reductive linear algebraic group. The…
On intersection cohomology with torus actions of complexity one
Marta Agustin Vicente, Kevin Langlois
The purpose of this article is to investigate the intersection cohomology for algebraic varieties with torus action. Given an algebraic torus , one of our result determ…
On the geometry of normal horospherical G-varieties of complexity one
Kevin Langlois, Ronan Terpereau
Let G be a connected simply-connected reductive algebraic group. In this article, we consider the normal algebraic varieties equipped with a horospherical G-action such that the qu…
Additive group actions on affine T-varieties of complexity one in arbitrary characteristic
Kevin Langlois, Alvaro Liendo
Let X be a normal affine T-variety of complexity at most one over a perfect field k, where T stands for the split algebraic torus. Our main result is a classification of additive g…
Demazure roots and spherical varieties: the example of horizontal SL(2)-actions
Kevin Langlois, Alexander Perepechko
Let be a connected reductive group, and let be an affine -spherical variety. We show that the classification of -actions on normalized by can be…
Polyhedral divisors and torus actions of complexity one over arbitrary fields
Kevin Langlois
We show that the presentation of affine -varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We also describe a class of multigra…