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

Hitching, George Harry
Journal article, Peer reviewed
Accepted version
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inflection_Segre_Hitching_Geom_Dedicata_revised.pdf (1002.Kb)
URI
https://hdl.handle.net/10642/8367
Date
2019-06-26
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  • LUI - Institutt for grunnskole- og faglærerutdanning [490]
Original version
Hitching. Quot schemes, Segre invariants, and inflectional loci of scrolls over curves. Geometriae Dedicata. 2019   https://dx.doi.org/10.1007/s10711-019-00463-z
Abstract
Let E be a vector bundle over a smooth curve C, and S = PE the associated projective bundle. We describe the inflectional loci of certain projective models ψ: S 99K Pn in terms of Quot schemes of E. This gives a geometric characterisation of the Segre invariant s1(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 ψ, the inflectional loci are all of the expected dimension. An auxiliary result, valid for a general subvariety of Pn, is that under mild hypotheses, the inflectional loci associated to a projection from a general centre are of the expected dimension.
Publisher
Springer
Series
Geometriae Dedicata;
Journal
Geometriae Dedicata

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