Complex and Symplectic Geometry

This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

1 Generalized Connected Sum Constructions for Resolutions of Extremal and KCSC Orbifolds.- 2 Ohsawa-Takegoshi Extension Theorem for Compact Kähler Manifolds And Applications.- 3 TBA.- 4 The Monge-Ampère Energy Class E.- 5 Quasi-Negative Holomorphic Sectional Curvature and Ampleness of the Canonical Class.- 6 Surjective Holomorphic Maps onto Oka Manifolds.- 7 Stabilized Symplectic Embeddings.- 8 On the Obstruction of the Deformation Theory in the DGLA of Graded Derivations.- 9 Cohomologies On Hypercomplex Manifolds.- 10 The Teichmüller Stack.- 11 Embedding of LCK Manifolds with Potential into HOPF Manifolds using Riesz-Schauder Theorem.- 12 Orbits of Real Forms, Matsuki Duality and CR-Cohomology.- 13 Generalized Geometry of Norden and Para Norden Manifolds.- 14 Spectral and Eigenfunction Asymptotics in Toeplitz Quantization.- 15 On Bi-Hermitian Surfaces.- 16 Kähler-Einstein Metrics on Q-Smoothable Fano Varieties, their Moduli and some Applications.- 17 Cohomological Aspects on Complex and Symplectic Manifolds.- 18 Towards the Classification of Class VII Surfaces.