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DELIGNE PAIRINGS AND FAMILIES OF RANK ONE LOCAL SYSTEMS ON ALGEBRAIC CURVES
DELIGNE PAIRINGS LOCAL SYSTEMS ALGEBRAIC CURVES
2015/12/17
For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, ...
Modern scientific technology is providing a new class of large-scale simultaneous
inference problems, with hundreds or thousands of hypothesis tests to consider at the
same time. Microarrays e...
Local invariants on quotient singularities and a genus formula for weighted plane curves
Local invariants quotient singularities genus formula weighted plane curves Algebraic Geometry
2012/6/30
In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. A generalization of the local {\delta}-inv...
Constructing higher dimensional local fields
Constructing higher dimensional local fields Algebraic Geometry
2012/4/18
This note is a gentle introduction to higher dimensional local fields, with the motivating problem being the standard geometric "localisation-completion" process by which they can be constructed. A di...
The Local Structure of Compactified Jacobians: Deformation Theory
Compactified Jacobian compactified Picard scheme nodal curve torsion-free sheaf
2011/9/16
Abstract: This paper studies the local geometry of compactified Jacobians constructed by Caporaso, Oda-Seshadri, Pandharipande, and Simpson. The main result is a presentation of the completed local ri...
VersalDeformations - a package for computing versal deformations and local Hilbert schemes
VersalDeformations local Hilbert schemes versal deformations Algebraic Geometry
2011/9/5
Abstract: We provide an overview of the Macaulay2 package VersalDeformations, which algorithmically computes versal deformations of isolated singularities, as well as local (multi)graded Hilbert schem...
In 70's there was discovered a construction how to attach to some algebraic-geometric data an infinite-dimensional subspace in the space k((z)) of the Laurent power series. The construction is known a...