269 research outputs found
A normal form algorithm for the Brieskorn lattice
This article describes a normal form algorithm for the Brieskorn lattice of
an isolated hypersurface singularity. It is the basis of efficient algorithms
to compute the Bernstein-Sato polynomial, the complex monodromy, and
Hodge-theoretic invariants of the singularity such as the spectral pairs and
good bases of the Brieskorn lattice. The algorithm is a variant of Buchberger's
normal form algorithm for power series rings using the idea of partial standard
bases and adic convergence replacing termination.Comment: 23 pages, 1 figure, 4 table
Good bases for tame polynomials
An algorithm to compute a good basis of the Brieskorn lattice of a
cohomologically tame polynomial is described. This algorithm is based on the
results of C. Sabbah and generalizes the algorithm by A. Douai for convenient
Newton non-degenerate polynomials.Comment: 28 pages, 0 figures, http://www.mathematik.uni-kl.de/~mschulz
Linear free divisors and Frobenius manifolds
We study linear functions on fibrations whose central fibre is a linear free divisor. We analyse the Gauß–Manin system associated to these functions, and prove the existence of a primitive and homogenous form. As a consequence, we show that the base space of the semi-universal unfolding of such a function carries a Frobenius manifold structure
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