Carlos T. Simpson
Fixed points and lines in 2-metric spaces.
Wed, 03/31/2010 - 15:01 — SomNambulAuthors: Carlos T. Simpson, Abdelkrim Aliouche
Subjects: Metric Geometry
AbstractWe consider bounded 2-metric spaces satisfying an additional axiom, and show
that a contractive mapping has either a fixed point or a fixed line.Homotopy theory of higher categories.
Mon, 01/25/2010 - 16:01 — SomNambulAuthors: Carlos T. Simpson
Subjects: Category Theory
AbstractThis is the first draft of a book about higher categories approached by
iterating Segal's method, as in Tamsamani's definition of $n$-nerve and
Pelissier's thesis. If $M$ is a tractable left proper cartesian model category,
we construct a tractable left proper cartesian model structure on the category
of $M$-precategories. The procedure can then be iterated, leading to model
categories of $(\infty, n)$-categories.Obstructed bundles of rank two on a quintic surface.
Thu, 09/10/2009 - 10:12 — SomNambulAuthors: Nicole Mestrano, Carlos T. Simpson
Subjects: Algebraic Geometry
AbstractIn this note we consider the moduli space of stable bundles of rank two on a
very general quintic surface. We study the obstructed points of the moduli
space via the spectral covering of a twisted endomorphism. This analysis leads
in some examples to a generically non-reduced component of the moduli space,
and a component which is generically smooth of one bigger than the expected
dimension. We obtain a sharp bound asked for by O'Grady saying when the moduli
space is good.Obstructed bundles of rank two on a quintic surface.
Thu, 09/10/2009 - 10:12 — SomNambulAuthors: Nicole Mestrano, Carlos T. Simpson
Subjects: Algebraic Geometry
AbstractIn this note we consider the moduli space of stable bundles of rank two on a
very general quintic surface. We study the obstructed points of the moduli
space via the spectral covering of a twisted endomorphism. This analysis leads
in some examples to a generically non-reduced component of the moduli space,
and a component which is generically smooth of one bigger than the expected
dimension. We obtain a sharp bound asked for by O'Grady saying when the moduli
space is good.
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