111,424 research outputs found
Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields
We prove the existence of non-positively curved K\"ahler-Einstein metrics
with cone singularities along a given simple normal crossing divisor on a
compact K\"ahler manifold, under a technical condition on the cone angles, and
we also discuss the case of positively-curved K\"ahler-Einstein metrics with
cone singularities. As an application we extend to this setting classical
results of Lichnerowicz and Kobayashi on the parallelism and vanishing of
appropriate holomorphic tensor fields.Comment: 36 pages, v3: added a section on the log-Fano case. To appear in
Annales Scientifiques de l'EN
EL-Shellability and Noncrossing Partitions Associated with Well-Generated Complex Reflection Groups
In this article we prove that the lattice of noncrossing partitions is
EL-shellable when associated with the well-generated complex reflection group
of type , for , or with the exceptional well-generated
complex reflection groups which are no real reflection groups. This result was
previously established for the real reflection groups and it can be extended to
the well-generated complex reflection group of type , for , as well as to three exceptional groups, namely and
, using a braid group argument. We thus conclude that the lattice of
noncrossing partitions of any well-generated complex reflection group is
EL-shellable. Using this result and a construction by Armstrong and Thomas, we
conclude further that the poset of -divisible noncrossing partitions is
EL-shellable for every well-generated complex reflection group. Finally, we
derive results on the M\"obius function of these posets previously conjectured
by Armstrong, Krattenthaler and Tomie.Comment: 37 pages, 4 figures. Moved the technical details of the proof of the
EL-shellability of to the appendix. More references adde
Construction of Hamiltonian-minimal Lagrangian submanifolds in complex Euclidean space
We describe several families of Lagrangian submanifolds in the complex
Euclidean space which are H-minimal, i.e. critical points of the volume
functional restricted to Hamiltonian variations. We make use of various
constructions involving planar, spherical and hyperbolic curves, as well as
Legendrian submanifolds of the odd-dimensional unit sphere.Comment: 23 pages, 5 figures, Second version. Changes in statement and proof
of Corollary
Connectivity Properties of Factorization Posets in Generated Groups
We consider three notions of connectivity and their interactions in partially
ordered sets coming from reduced factorizations of an element in a generated
group. While one form of connectivity essentially reflects the connectivity of
the poset diagram, the other two are a bit more involved: Hurwitz-connectivity
has its origins in algebraic geometry, and shellability in topology. We propose
a framework to study these connectivity properties in a uniform way. Our main
tool is a certain linear order of the generators that is compatible with the
chosen element.Comment: 35 pages, 17 figures. Comments are very welcome. Final versio
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