Quot schemes, Segre invariants, and inflectional loci of scrolls over\n curves

2018/12/03 by George H. Hitching, Hitching, George H.
Mathematics · #14H60 #14N05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1812.00706

openalex publication_date 2018/12/03 · openalex created_date 2022/08/01 · openalex updated_date 2026/07/28

Abstract

Let E be a vector bundle over a smooth curve C, and S = \ℙ E\nthe associated projective bundle. We describe the inflectional loci of certain\nprojective models \ψ colon S dashrightarrow \ℙⁿ in terms of Quot\nschemes of E. This gives a geometric characterisation of the Segre invariant\ns₁ (E), which leads to new geometric criteria for semistability and\ncohomological stability of bundles over C. We also use these ideas to show\nthat for general enough S and \ψ, the inflectional loci are all of the\nexpected dimension. An auxiliary result, valid for a general subvariety of\n\ℙⁿ, is that under mild hypotheses, the inflectional loci associated\nto a projection from a general centre are of the expected dimension.\n

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