Relative Bott-Samelson varieties. (English) Zbl 1527.14101
Summary: We prove that, defined with respect to versal flags, the product of two relative Bott-Samelson varieties over a flag bundle is a resolution of singularities of a relative Richardson variety. This result generalizes Brion’s resolution of singularities of Richardson varieties to the relative setting. As an application, this gives a resolution of singularities, with a modular interpretation, for the Brill-Noether variety with imposed ramification on twice-marked elliptic curves.
MSC:
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
| 14E15 | Global theory and resolution of singularities (algebro-geometric aspects) |
Keywords:
Bott-Samelson variety; relative Richardson variety; Brill-Noether variety; resolution of singularitiesReferences:
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