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Curves, Algebraic. --- Projective spaces. --- Geometry, Projective. --- Courbes algébriques. --- Espaces projectifs. --- Géométrie projective. --- Courbes algébriques --- Espaces projectifs --- Géométrie projective --- Curves, Algebraic --- Projective spaces --- Geometry, Projective --- Algebraic curves --- Algebraic varieties --- Spaces, Projective --- Projective geometry --- Geometry, Modern

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Given n general points p_1, p_2, ldots , p_n in mathbb P^r, it is natural to ask when there exists a curve C subset mathbb P^r, of degree d and genus g, passing through p_1, p_2, ldots , p_n. In this paper, the authors give a complete answer to this question for curves C with nonspecial hyperplane section. This result is a consequence of our main theorem, which states that the normal bundle N_C of a general nonspecial curve of degree d and genus g in mathbb P^r (with d geq g + r) has the property of interpolation (i.e. that for a general effective divisor D of any degree on C, either H^0(N_C(-D)) = 0 or H^1(N_C(-D)) = 0), with exactly three exceptions.

Curves, Algebraic. --- Projective spaces. --- Geometry, Projective.

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This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact

Science: general issues --- Pharmacology --- Ethnopharmacology --- phytochemistry --- Molecular Pharmacology --- Natural Products

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