Poisson structures on Calabi-Yau threefolds and their deformations

• Grant number: 21/11750-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2022
• End date: April 30, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ivan Struchiner
• Grantee: Bruno Suzuki
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The central problem in any area of mathematics is the classification of the objects of interest modulo isomorphism. For example, in differential geometry one wishes to classify real manifolds modulo real smooth diffeomorphisms, while in complex geometry one wishes to classify complex manifolds modulo holomorphic diffeomorphisms.Deformation theory is the local counterpart of this question, where one studies how the isomorphism classes react to small modification of the initial data. This project aims to study the Poisson structures of the Calabi-Yau threefolds which are total spaces of rank-2 vector bundles over the complex projective space and compare them with the ones on their (infinite-dimensional families of) commutative deformations.The proposed topics of study are their Poisson cohomologies and symplectic foliations, together with obtaining and understanding of the structure of the moduli spaces of Poisson structures, and how all of these geometric structures change under the effect of the deformations.