Logarithmic Comparison Theorem versus Gauss–manin System for Isolated Singularities

Logarithmic vector fields and multiplication table

Susumu TANABÉ Abstract. This is a review article on the Gauss-Manin system associated to the complete intersection singularities of projection. We show how the logarithmic vector fields appear as coefficients to the Gauss-Manin system (Theorem 2.7). We examine further how the multiplication table on the Jacobian quotient module calculates the logarithmic vector fields tangent to the discriminan...

Susumu Tanabé

Susumu TANABÉ Abstract. This is a review article on the Gauss-Manin system associated to the complete intersection singularities of projection. We show how the logarithmic vector fields appear as coefficients to the Gauss-Manin system (Theorem 2.7). We examine further how the multiplication table on the Jacobian quotient module calculates the logarithmic vector fields tangent to the discriminan...

ar X iv : m at h / 99 06 12 9 v 1 [ m at h . A G ] 1 8 Ju n 19 99 ALGEBRAIC GAUSS - MANIN SYSTEMS AND BRIESKORN MODULES

We study the algebraic Gauss-Manin system and the algebraic Brieskorn module associated to a polynomial mapping with isolated singularities. Since the algebraic GaussManin system does not contain any information on the cohomology of singular fibers, we construct a non quasi-coherent sheaf which gives the cohomology of every fiber. Then we study the algebraic Brieskorn module by comparing it wit...

Algorithmic Gauss-Manin Connection Algorithms to Compute Hodge-theoretic Invariants of Isolated Hypersurface Singularities

ar X iv : m at h / 99 06 12 9 v 2 [ m at h . A G ] 1 4 D ec 1 99 9 ALGEBRAIC GAUSS - MANIN SYSTEMS AND BRIESKORN MODULES

We study the algebraic Gauss-Manin system and the algebraic Brieskorn module associated to a polynomial mapping with isolated singularities. Since the algebraic GaussManin system does not contain any information on the cohomology of singular fibers, we first construct a non quasi-coherent sheaf which gives the cohomology of every fiber. Then we study the algebraic Brieskorn module, and show tha...