Abstract
Let E be a vector bundle over a smooth curve C, and $$S = {{\mathbb {P}}}E$$ the associated projective bundle. We describe the inflectional loci of certain projective models $$\psi :S \dashrightarrow {{\mathbb {P}}}^n$$ in terms of Quot schemes of E. This gives a geometric characterisation of the Segre invariant $$s_1 (E)$$, which leads to new geometric criteria for semistability and cohomological stability of bundles over C. We also use these ideas to show that for general enough S and $$\psi $$, the inflectional loci are all of the expected dimension. An auxiliary result, valid for a general subvariety of $${{\mathbb {P}}}^n$$, is that under mild hypotheses, the inflectional loci associated to a projection from a general centre are of the expected dimension.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.