Bourbaki modules and the module of Jacobian derivations of projective hypersurfaces

2025/06/30 by Alexandru Dimca, Gabriel Sticlaru, Dimca, Alexandru +1 · 1 citation
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2506.23950

openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two properties of projective hypersurfaces related to the module of Jacobian derivations, namely being tame and being plus-one generated, are discussed in this paper. Tame hypersurfaces are related to Bourbaki ideals, and free hypersurfaces are the simplest examples of tame hypersurfaces. Plus-one generated hypersurfaces are the non free hypersurfaces which are closest to the free ones, and it is an open question whether all of them are tame.

Citations

• The Bourbaki Degree of Plane Projective Curves
• Graded Bourbaki ideals of graded modules
• Quasi-complete intersections in P2 and syzygies
• Quasi complete intersections and global Tjurina number of plane curves
• Plus-one generated and next to free arrangements of hyperplanes
• On the jumping lines of bundles of logarithmic vector fields along plane curves
• On supersolvable and nearly supersolvable line arrangements
• Homology of Homogeneous Divisors
• Plane Cremona maps: saturation and regularity of the base ideal
• The Jacobian ideal of a hyperplane arrangement
• Elementary modifications and line configurations in P²

Cited by

• Bourbaki degree of pairs of projective surfaces

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