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arXiv · 1904.00686

Versality, bounds of global Tjurina numbers and logarithmic vector fields along hypersurfaces with isolated singularities

Alexandru Dimca
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Abstract

We recall first the relations between the syzygies of the Jacobian ideal of the defining equation for a projective hypersurface $V$ with isolated singularities and the versality properties of $V$, as studied by du Plessis and Wall. Then we show how the bounds on the global Tjurina number of $V$ obtained by du Plessis and Wall lead to substantial improvements of our previous results on the stability of the reflexive sheaf $T\langle V\rangle$ of logarithmic vector fields along $V$, and on the Torelli property in the sense of Dolgachev-Kapranov of $V$.

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Alexandru Dimca. 2019-04-01. Versality, bounds of global Tjurina numbers and logarithmic vector fields along hypersurfaces with isolated singularities. https://arxiv.org/abs/1904.00686

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