Complex and Symplectic Geometry, 1st ed. 2017 Springer INdAM Series, Vol. 21

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.

Adriano Tomassini received his Ph.D. in Mathematics at the University of Forence in 1997. He was assistant professor at the University of Palermo and then at the University of Parma, where he is currently professor of geometry. He has visited the Universities of Michigan, Minnesota, Notre Dame and Stanford. His research interests are in complex, symplectic and differential geometry. He is the author of around 55 publications.

Costantino Medori received his Ph.D. in Mathematics at the International School for Advanced Studies (Trieste, Italy) in 1996. He was a postdoc at the University of Pisa and then a researcher at the University of Parma, where he is currently professor of geometry. His research interests are in differential and complex geometry, more specifically in CR geometry. He is the author of around 30 publications.

Presents contributions from leading experts and emerging researchers in the field of complex and symplectic geometry

Provides up-to-date overviews on current topics in the field

Provides an excellent introduction to the field, aimed at a wide readership