Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such collections of varieties: their minimal degree and their maximal number of linearly independent smallest degree hypersurfaces passing through them. We show results for curves and surfaces, and pose several questions.

Minimal degree equations for curves and surfaces (variations on a theme of Halphen) / Ballico, E.; Ventura, E.. - In: BEITRAGE ZUR ALGEBRA UND GEOMETRIE. - ISSN 0138-4821. - 61:2(2020), pp. 297-315. [10.1007/s13366-019-00471-w]

Minimal degree equations for curves and surfaces (variations on a theme of Halphen)

Ventura E.
2020

Abstract

Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such collections of varieties: their minimal degree and their maximal number of linearly independent smallest degree hypersurfaces passing through them. We show results for curves and surfaces, and pose several questions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2958145