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Inflectional loci of scrolls

Authors:	Antonio Lanteri Raquel Mallavibarrena Ragni Piene

Institution:	(1) Dipartimento di Matematica “F. Enriques”, Università di Milano, Via C. Saldini, 50, 20133 Milan, Italy;(2) Departamento de Algebra, Facultad de Matemáticas, Universidad Complutense de Madrid, Ciudad Universitaria, 28040 Madrid, Spain;(3) CMA and Department of Mathematics, University of Oslo, PO Box 1053, Blindern, 0316 Oslo, Norway

Abstract:	Let $X \subset \mathbb{P}^{N}$ be a scroll over a smooth curve C and let $\mathcal{L}={\mathcal{O}}_{\mathbb{P}^{N}}(1)\|_X$ denote the hyperplane bundle. The special geometry of X implies that certain sheaves related to the principal part bundles of $\mathcal{L}$ are locally free. The inflectional loci of X can be expressed in terms of these sheaves, leading to explicit formulas for the cohomology classes of the loci. The formulas imply that the only uninflected scrolls are the balanced rational normal scrolls.

Keywords:	Scroll Inflectional locus Principal parts bundle
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