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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...
This article is motivated by the need for better understanding of refined Riemann-Roch theorems and the behavior of the determinant of the cohomology. This poses a certain problem of functoriality and...
Macdonald formula for curves with planar singularities
Macdonald formula planar singularities curves Algebraic Geometry
2011/9/1
Abstract: We generalize Macdonald's formula for the cohomology of Hilbert schemes of points on a curve from smooth curves to curves with planar singularities: we relate the cohomology of the Hilbert s...
On Colmez's product formula for periods of CM-abelian varieties
Fermat curve stable reduction product formula
2011/8/25
Abstract: Colmez conjectured a product formula for periods of abelian varieties with complex multiplication by a field K, analogous to the standard product formula in algebraic number theory. He prove...
A Riemann theta function formula with its application to double periodic wave solutions of nonlinear equations
Riemann theta function Hirota's bilinear form nonlinear equations
2010/4/1
Based on a Riemann theta function and Hirota's bilinear form, a lucid and straightforward way is presented to explicitly construct double periodic wave solutions for both nonlinear differential and di...