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On linearly normal strange curves

Edoardo Ballico (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Here we prove a numerical bound implying that, except for smooth plane conics in characteristic 2, no complete linear system maps birationally a smooth curve into a projective space with a strange curve as image.

On Noether and strict stability, Hilbert exponent, and relative Nullstellensatz

Chia-chi Tung (2013)

Annales Polonici Mathematici

Conditions characterizing the membership of the ideal of a subvariety arising from (effective) divisors in a product complex space Y × X are given. For the algebra Y [ V ] of relative regular functions on an algebraic variety V, the strict stability is proved, in the case where Y is a normal space, and the Noether stability is established under a weakened condition. As a consequence (for both general and complete intersections) a global Nullstellensatz is derived for divisors in Y × N , respectively, Y × N ( ) . Also...

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