Inflectional loci of scrolls

Details Inflectional loci of scrolls Inflectional loci of scrolls

2006-12-14

arxiv.org/abs/math/0612403v2

Mathematics

Algebraic Geometry

9 pages, improved version. Accepted in Mathematische Zeitschrift

Scientific paper

Let $X\subset \mathbb P^N$ be a scroll over a smooth curve $C$ and let $\L=\mathcal O_{\mathbb P^N}(1)|_X$ denote the hyperplane bundle. The special geometry of $X$ implies that some sheaves related to the principal part bundles of $\L$ 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.

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