Euler classes for elliptic pairs

Schapira, Pierre; Schneiders, Jean-Pierre

doi:10.1515/9783110856033.1

Cited by 2 publications

(3 citation statements)

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“…Proof. We refer to [SS94,Theorem 4.2 and Corollary 4.3] for the proof of part (ii) (or one can adapt the proof of [Kas03,Theorems 4.25 and 4.27]), whereas for the proof of part (i) we can easily adapt the argument of [LS87, Proposition 2.1] which gives the absolute case.…”

Section: Bmentioning

confidence: 99%

Relative regular Riemann–Hilbert correspondence II

Fiorot¹,

Fernandes²,

Sabbah³

2023

Compositio Math.

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We develop the theory of relative regular holonomic $\mathcal {D}$ -modules with a smooth complex manifold $S$ of arbitrary dimension as parameter space, together with their main functorial properties. In particular, we establish in this general setting the relative Riemann–Hilbert correspondence proved in a previous work in the one-dimensional case.

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Section: Bmentioning

confidence: 99%

Relative regular Riemann–Hilbert correspondence II

Fiorot¹,

Fernandes²,

Sabbah³

2023

Compositio Math.

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“…So if F is also a subanalytically constructible sheaf complex, one gets that (F, G) is an elliptic pair in the sense of [27].…”

Section: Splayed Constructible Functionsmentioning

confidence: 99%

“…In [18] a counterpart of Corollary 3.5 in the context of real geometry is discussed under a "stratified tranversality" assumption. See also [27][(1.4), Part II] for a far reaching generalization to elliptic pairs. Note that both references use a different orientation convention, so that the sign (−1) m in (3.21) disappears.…”

Section: Pullback Of Lagrangian Cyclesmentioning

confidence: 99%

Chern Classes and Transversality for Singular Spaces

Schürmann¹

2017

Trends in Mathematics

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In this paper we compare different notions of transversality for possible singular complex algebraic or analytic subsets of an ambient complex manifold and prove a refined intersection formula for their Chern-Schwartz-MacPherson classes. In case of a transversal intersection of complex Whitney stratified sets, this result is well known. For splayed subsets it was conjectured (and proven in some cases) by Aluffi and Faber. Both notions are stronger than a micro-local "non-characteristic intersection" condition for the characteristic cycles of (associated) constructible functions, which nevertheless is enough to imply the asked refined intersection formula for the Chern-Schwartz-MacPherson classes. The proof is based the multiplicativity of Chern-Schwartz-MacPherson classes with respect to cross products, as well as a new Verdier-Riemann-Roch theorem for "non-characteristic pullbacks".

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Euler classes for elliptic pairs

Cited by 2 publications

References 0 publications

Relative regular Riemann–Hilbert correspondence II

Relative regular Riemann–Hilbert correspondence II

Chern Classes and Transversality for Singular Spaces

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