Isotropic Kempf--Laksov flag bundles
Lionel Darondeau
TL;DR
This paper introduces new flag bundle constructions related to Kempf--Laksov desingularizations in symplectic and orthogonal Grassmann bundles, providing universal formulas for their Gysin maps.
Contribution
It presents novel analogs of Kempf--Laksov desingularizations for symplectic and orthogonal Grassmann bundles, extending their geometric and algebraic understanding.
Findings
Constructed flag bundles as chains of zero-loci of regular sections.
Derived universal Gysin formulas for isotropic Schubert bundles.
Provided descriptions of these bundles as birational to Schubert bundles.
Abstract
We introduce analogs of the Kempf--Laksov desingularizations of Schubert bundles in (non-necessary Lagrangian) symplectic Grassmann bundles. In this setting, these are (possibly singular) irreducible flag bundles that are birational to Schubert bundles, and can be described as chains of zero-loci of regular sections in projectivized bundles. The orthogonal analogs are also presented. We immediatly derive universal Gysin formulas for isotropic Schubert bundles from these very constructions.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology