Search results for: Pietro De Poi

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article

On the hypersurfaces contained in their Hessian

Pietro De Poi, Giovanna Ilardi

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2019 > 18 > 21-33

This article presents the theory of focal locus applied to the hypersurfaces in the projective space which are (finitely) covered by linear spaces and such that the tangent space is constant along these spaces.

article

On the hypersurfaces contained in their Hessian

Pietro De Poi, Giovanna Ilardi

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2019 > 18

article

On higher Gauss maps

Pietro De Poi, Giovanna Ilardi

Journal of Pure and Applied Algebra > 2015 > 219 > 11 > 5137-5148

We prove that the general fibre of the i-th Gauss map has dimension m if and only if at the general point the (i+1)-th fundamental form consists of cones with vertex a fixed Pm−1, extending a known theorem for the usual Gauss map. We prove this via a recursive formula for expressing higher fundamental forms. We also show some consequences of these results.

article

On first order congruences of lines of 4 with a fundamental curve

Pietro De Poi

manuscripta mathematica > 2001 > 106 > 1 > 101-116

Abstract: We discuss projective families of lines of n, and in particular congruences of order one. After giving general results, we obtain a complete classification of the case of 4 in which there is a fundamental curve.

article

On first order congruences of lines of ℙ4 with a fundamental curve

Pietro De Poi

manuscripta mathematica > 2001 > 106 > 1 > 101-116

We discuss projective families of lines of ℙⁿ, and in particular congruences of order one. After giving general results, we obtain a complete classification of the case of ℙ⁴ in which there is a fundamental curve.

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Search results for: Pietro De Poi

On the hypersurfaces contained in their Hessian

On the hypersurfaces contained in their Hessian

On higher Gauss maps

On first order congruences of lines of 4 with a fundamental curve

On first order congruences of lines of ℙ4 with a fundamental curve

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