IUMJ

Title: Inflectional loci of scrolls over smooth, projective varieties

Authors: Raquel Mallavibarrena, Antonio Lanteri and Ragni Piene

Issue: Volume 61 (2012), Issue 2, 717-750

Abstract:

Let $X\subset\mathbb{P}^N$ be a scroll over an $m$-dimensional variety $Y$. We find the locally free sheaves on $X$ governing the osculating behavior of $X$, and, under certain dimension assumptions, we compute the cohomology class and the degree of the inflectional locus of $X$. The case $m = 1$ was treated in [A. Lanteri, R. Mallavibarrena, and R. Piene, \textit{Inflectional loci of scrolls}, Math. Z. \textbf{258} (2008), no. 3, 557--564]. Here we treat the case $m \ge 2$, which is more complicated for at least two reasons: the expression for the osculating sheaves and the computations of the class of the inflectional locus become more complex, and the dimension requirements needed to ensure validity of the formulas are more severe.