Symmetries and stabilization for sheaves of vanishing cycles

Christopher Brav, Vittoria Bussi, Delphine Dupont, Dominic Joyce, and Balázs Szendrői,
with an Appendix by Jörg Schürmann

Journal of Singularities
volume 11 (2015), 85-151

Received: 18 December 2013. Received in revised form: 20 May 2015.

DOI: 10.5427/jsing.2015.11e

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We study symmetries and stabilization properties of perverse sheaves of vanishing cycles of a regular function on a smooth C-scheme. We also generalize our results to replace the smooth scheme by a complex analytic space, and consider D-modules or mixed Hodge modules. We discuss applications to categorifying Donaldson--Thomas invariants of Calabi-Yau 3-folds, and to defining a 'Fukaya category' of Lagrangians in a complex symplectic manifold using perverse sheaves.

Author(s) information:

Christopher Brav, Faculty of Mathematics, Higher School of Economics, 7 Vavilova Str., Moscow, Russia

Vittoria Bussi, ICTP, Strada Costiera 11, Trieste, Italy

Delphine Dupont, Dominic Joyce and Balázs Szendrői, The Mathematical Institute, Woodstock Road, Oxford, UK

Jörg Schürmann, Mathematische Institut, Universität Münster, Einsteinstrasse62, 48149 Münster, Germany