On the geometry of algebraic curves having many real components.

Let C ⊆ P be an unramified nonspecial real space curve having many real branches and few ovals. We show that C is a rational normal curve if n is even, and that C is an M-curve having no ovals if n is odd.

Halphen's gaps for space curves of submaximum genus

Alberto Dolcetti (1988)

Bulletin de la Société Mathématique de France

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Postulation and gonality for projective curves

Edoardo Ballico (1988)

Rendiconti del Seminario Matematico della Università di Padova

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Irreducibility of some families of linear series with Brill-Noether number. I

David Eisenbud, Joe Harris (1989)

Annales scientifiques de l'École Normale Supérieure

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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

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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.