The computation of the logarithmic cohomology for plane curves

DOI10.1016/j.jalgebra.2009.03.039zbMath1186.14061arXiv0712.0001OpenAlexW2027949105MaRDI QIDQ2267442

Nobuki Takayama, Francisco-Jesús Castro-Jiménez

Publication date: 1 March 2010

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.0001

zbMATH Keywords

D-modulesGrobner basislogarithmic cohomologyalgrebraic geometry

Mathematics Subject Classification ID

Computational aspects of algebraic curves (14Q05) de Rham cohomology and algebraic geometry (14F40)

Related Items (1)

Nilpotency in arc scheme of plane curves

Uses Software

• Kan
• D-modules

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algorithms for the Quillen-Suslin theorem
• An algorithm for de Rham cohomology groups of the complement of an affine variety via \(D\)-module computation
• Algorithms for \(b\)-functions, restrictions, and algebraic local cohomology groups of \(D\)-modules
• Logarithmic cohomology of the complement of a plane curve
• Gröbner deformations of hypergeometric differential equations
• Logarithmic differential operators and logarithmic de rham complexes relative to a free divisor
• Testing the Logarithmic Comparison Theorem for Free Divisors
• Cohomology of the complement of a free divisor
• Algorithms for \(D\)-modules -- restriction, tensor product, localization, and local cohomology groups
• Polynomial and rational solutions of holonomic systems
• Computing the cup product structure for complements of complex affine varieties.
• Minimal free resolutions of homogenized \(D\)-modules
• Computing homomorphisms between holonomic \(D\)-modules
• Explicit comparison theorems for \(\mathcal D\)-modules

This page was built for publication: The computation of the logarithmic cohomology for plane curves