Bourbaki modules and the module of Jacobian derivations of projective hypersurfaces
Alexandru Dimca, Gabriel Sticlaru
TL;DR
This paper explores properties of projective hypersurfaces related to Jacobian derivations, focusing on tameness and plus-one generation, and their connections to Bourbaki modules and ideals.
Contribution
It introduces the concepts of tame and plus-one generated hypersurfaces, analyzing their properties and relationships, and discusses open questions about their tameness.
Findings
Tame hypersurfaces relate to Bourbaki ideals.
Free hypersurfaces are the simplest tame examples.
Open question on whether all plus-one generated hypersurfaces are tame.
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.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation · Commutative Algebra and Its Applications