Segre numbers s_P for principal G-bundles over curves are semicontinuous, define moduli stratifications, relate under surjective homomorphisms, and satisfy a Hirschowitz-type bound for the Borel subgroup of GL_3.
: Schematic Harder-Narasimhan stratification , Internat.\ J.\ Math.\ 22, no.\ 10 (2011), 1365--1373
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Segre invariants of principal bundles over a curve
Segre numbers s_P for principal G-bundles over curves are semicontinuous, define moduli stratifications, relate under surjective homomorphisms, and satisfy a Hirschowitz-type bound for the Borel subgroup of GL_3.