Duke Mathematical Journal

Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink

Gil Guibert, François Loeser, and Michel Merle

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We prove a motivic analogue of Steenbrink's conjecture [25, Conjecture 2.2] on the Hodge spectrum (proved by M. Saito in [21]). To achieve this, we construct and compute motivic iterated vanishing cycles associated with two functions. We are also led to introduce a more general version of the convolution operator appearing in the motivic Thom-Sebastiani formula. Throughout the article we use the framework of relative equivariant Grothendieck rings of varieties endowed with an algebraic torus action

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Duke Math. J., Volume 132, Number 3 (2006), 409-457.

First available in Project Euclid: 1 April 2006

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Primary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 14B07: Deformations of singularities [See also 14D15, 32S30] 14J17: Singularities [See also 14B05, 14E15] 32S05: Local singularities [See also 14J17] 32S25: Surface and hypersurface singularities [See also 14J17] 32S30: Deformations of singularities; vanishing cycles [See also 14B07] 32S35: Mixed Hodge theory of singular varieties [See also 14C30, 14D07] 32S55: Milnor fibration; relations with knot theory [See also 57M25, 57Q45]


Guibert, Gil; Loeser, François; Merle, Michel. Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink. Duke Math. J. 132 (2006), no. 3, 409--457. doi:10.1215/S0012-7094-06-13232-5. https://projecteuclid.org/euclid.dmj/1143935996

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