Singular improper affine spheres from agiven Lagrangian submanifold

Autor(es)

Craizer, Marcos ; Domitrz, Wojciech ; Rios, Pedro de M.

• Tipo de documento: Artigo Científico
• Fonte: ADVANCES IN MATHEMATICS; v. 374, p. 33-pg., 2020-11-18.

Resumo

Given a Lagrangian submanifold L of the affine symplectic 2n-space, one can canonically and uniquely define a center-chord and a special improper affine sphere of dimension 2n, both of whose sets of singularities contain L. Although these improper affine spheres (IAS) always present other singularities away from L(the off-shell singularities studied in [8]), they may also present singularities other than Lwhich are arbitrarily close to L, the so called singularities "on shell". These on-shell singularities possess a hidden Z(2) symmetry that is absent from the off-shell singularities. In this paper, we study these canonical IAS obtained from Land their onshell singularities, in arbitrary even dimensions, and classify all stable Lagrangian/Legendrian singularities on shell that may occur for these IAS when Lis a curve or a Lagrangian surface. (C) 2020 The Authors. Published by Elsevier Inc. (AU)

• Processo FAPESP: 15/02029-1 - Geometria simplética e a correspondência clássica-quântica
• Beneficiário: Pedro Paulo de Magalhaes Rios
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 16/09249-0 - Geometria afim e singularidades Lagrangianas-Legendrianas
• Beneficiário: Pedro Paulo de Magalhaes Rios
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional