A^1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections
arXiv:2002.01848
Abstract
We equate various Euler classes of algebraic vector bundles, including those of [BM, KW, DJK], and one suggested by M.J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class, and give formulas for local indices at isolated zeros, both in terms of 6-functor formalism of coherent sheaves and as an explicit recipe in commutative algebra of Scheja and Storch. As an application, we compute the Euler classes associated to arithmetic counts of d-planes on complete intersections in P^n in terms of topological Euler numbers over R and C.
arXiv commentCorrected statement and proof of Lemma 5.6 and Proposition 5.4
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- Quadratic types and the dynamic Euler number of lines on a quintic threefold
- Applications to A1-enumerative geometry of the A1-degree
- Computing A1-Euler numbers with Macaulay2
- Conics meeting eight lines over perfect fields
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