184 research outputs found
Flat parabolic vector bundles on elliptic curves
We describe the moduli space of logarithmic rank 2 connections on elliptic
curves with 2 poles.Comment: new version: fixed a sign in Proposition 2.
Characteristic Numbers and invariant subvarieties for Projective Webs
We define the characteristic numbers of a holomorphic k-distribution of any
dimension on and obtain relations between these numbers and the
characteristic numbers of an invariant subvariety. As an application we bound
the degree of a smooth invariant hypersurface
On the degree of Polar Transformations -- An approach through Logarithmic Foliations
We investigate the degree of the polar transformations associated to a
certain class of multi-valued homogeneous functions. In particular we prove
that the degree of the pre-image of generic linear spaces by a polar
transformation associated to a homogeneous polynomial is determined by the
zero locus of . For zero dimensional-dimensional linear spaces this was
conjecture by Dolgachev and proved by Dimca-Papadima using topological
arguments. Our methods are algebro-geometric and rely on the study of the Gauss
map of naturally associated logarithmic foliations
On automorphisms of moduli spaces of parabolic vector bundles
Fix general points , and a weight
vector of real numbers . Consider the moduli space parametrizing rank
two parabolic vector bundles with trivial determinant on which are semistable with respect to . Under
some conditions on the weights, we determine and give a modular interpretation
for the automorphism group of the moduli space . It
is isomorphic to for some
, and is generated by admissible elementary
transformations of parabolic vector bundles. The largest of these automorphism
groups, with , occurs for the central weight . The corresponding moduli space
is a Fano variety of dimension , which is
smooth if is odd, and has isolated singularities if is even.Comment: 13 page
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