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1 February 2019 Legendrian fronts for affine varieties
Roger Casals, Emmy Murphy
Duke Math. J. 168(2): 225-323 (1 February 2019). DOI: 10.1215/00127094-2018-0055

Abstract

In this article we study Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. First, we provide a systematic recipe for translating from a Weinstein Lefschetz bifibration to a Legendrian handlebody. Then we present several new applications of this technique to symplectic topology. This includes the detection of flexibility and rigidity for several families of Weinstein manifolds and the existence of closed, exact Lagrangian submanifolds. In particular, we prove that the Koras–Russell cubic is Stein deformation-equivalent to C3, and we verify the affine parts of the algebraic mirrors of two Weinstein 4-folds.

Citation

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Roger Casals. Emmy Murphy. "Legendrian fronts for affine varieties." Duke Math. J. 168 (2) 225 - 323, 1 February 2019. https://doi.org/10.1215/00127094-2018-0055

Information

Received: 8 February 2017; Revised: 30 June 2018; Published: 1 February 2019
First available in Project Euclid: 10 January 2019

zbMATH: 07036863
MathSciNet: MR3909897
Digital Object Identifier: 10.1215/00127094-2018-0055

Subjects:
Primary: 53D10
Secondary: 53D15, 57R17

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 2 • 1 February 2019
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