Research on generalized geometric structures, 4 dimensional differential topology and derived category

2015 Fiscal Year Final Research Report

• Project/Area Number: 25610011
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Osaka University
• Principal Investigator: Goto Ryushi 大阪大学, 理学(系)研究科(研究院), 教授 (30252571)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 一般化された複素構造 / 一般化されたケーラー構造 / ポアソン構造 / 変形理論 / モジュライ空間 / flat structure

Outline of Final Research Achievements

The author's results are mainly as follows. (1) We show that generalized complex structures on a complex surface induced from a holomorphic Poisson structure admit unobstructed deformations, i.e., the Kuranishi spaces are smooth. We construct moduli spaces of generalized complex structures induced from Poisson structures on del Pezzo surfaces. Further it turns out that the moduli space admits "Stratified flat structure", that is, the moduli space has a stratification which is constructed from the types of singularities of jumping locus and each strata admits a flat structure, i.e., a torsion free flat connection of the tangent bundle. (2) We obtain a new family of generalized complex structures with k connected components of jumping loci for any k on certain 4-manifolds which have neither complex structures and symplectic structures, by using logarithmic transformation of multiplicity m. These two results are already written in our paper [1] , [2] and they are accepted for publication.

Free Research Field

複素幾何、微分幾何