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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 immediately derive universal Gysin formulas for isotropic Schubert bundles from these very constructions.
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Lionel Darondeau (2024) studied this question.
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