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Bourbaki modules and the module of Jacobian derivations of projective hypersurfaces
Alexandru Dimca, Gabriel Sticlaru
https://arxiv.org/abs/2506.23950 http…

Bourbaki modules and the module of Jacobian derivations of projective hypersurfaces
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.

More about cofinally Bourbaki quasi-complete metric spaces
Argha Ghosh
https://arxiv.org/abs/2507.00541 https://arxiv.org/pdf/2507.00…

More about cofinally Bourbaki quasi-complete metric spaces
We characterize cofinally Bourbaki quasi-complete metric spaces and their completions in terms of certain Lipschitz-type functions. To this end, we introduce and study a new class of functions, namely strongly uniformly locally Lipschitz functions, which lie strictly between Lipschitz functions and uniformly locally Lipschitz functions. We show that a metric space is cofinally Bourbaki quasi-complete if and only if the class of strongly uniformly locally Lipschitz functions on coi…