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Sur les multiplicités de Schubert locales des faisceaux algébriques cohérents. (French) Zbl 0533.14023
Let X be a variety defined over an algebraically closed field k, \({\mathcal F}\) a coherent sheaf on X. For each \(x\in X\) and Schubert symbol a the local Schubert multiplicity \(e_ x({\mathcal F},a)\) is defined. If \({\mathcal F}=\Omega^ 1\!_ X\), one can express the local Euler obstruction of X at x as an alternating sum of these multiplicities. A formula is given, which yields in a special case one of Lê Dung Trang and B. Teissier [Ann. Math., II. Ser. 114, 457-491 (1981; Zbl 0488.32004)], thus generalizing this formula to varieties of arbitrary characteristic.
Reviewer: R.Piene
MSC:
14M15 Grassmannians, Schubert varieties, flag manifolds
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14B05 Singularities in algebraic geometry
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References:
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