952 research outputs found
Short antichains in root systems, semi-Catalan arrangements, and B-stable subspaces
Let \be be a Borel subalgebra of a complex simple Lie algebra \g. An
ideal of \be is called ad-nilpotent, if it is contained in [\be,\be]. The
generators of an ad-nilpotent ideal give rise to an antichain in the poset of
positive roots, and the whole theory can be expressed in a combinatorial
fashion, in terms of antichains. The aim of this paper is to present a
refinement of the enumerative theory of ad-nilpotent ideals for the case in
which \g has roots of different length. An antichain is called short, if it
consists of short roots. We obtain, for short antichains, analogues of all
results known for the usual antichains.Comment: LaTeX2e, 20 page
On IHS fourfolds with
The present work is concerned with the study of four-dimensional irreducible
holomorphic symplectic manifolds with second Betti number . We describe
their birational geometry and their relations to EPW sextics.Comment: to appear in Michigan Math.
Configurations of infinitely near points
We present a survey of some aspects and new results on configurations, i.e.
disjoint unions of constellations of infinitely near points, local and global
theory, with some applications and results on generalized Enriques diagrams,
singular foliations, and linear systems defined by clusters
Commutator estimates on contact manifolds and applications
This article studies sharp norm estimates for the commutator of
pseudo-differential operators with multiplication operators on closed
Heisenberg manifolds. In particular, we obtain a Calderon commutator estimate:
If is a first-order operator in the Heisenberg calculus and is
Lipschitz in the Carnot-Caratheodory metric, then extends to an
-bounded operator. Using interpolation, it implies sharp weak--Schatten
class properties for the commutator between zeroth order operators and H\"older
continuous functions. We present applications to sub-Riemannian spectral
triples on Heisenberg manifolds as well as to the regularization of a
functional studied by Englis-Guo-Zhang.Comment: 31 pages, improved presentation and additional reference
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