Birational Geometry and Moduli Spaces

This volume collects contributions from speakers at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the volume reflect the same idea, focusing on both these areas and their interaction. In particular, the book includes both surveys and original papers on irreducible holomorphic symplectic manifolds, Severi varieties, degenerations of Calabi-Yau varieties, uniruled threefolds, toric Fano threefolds, mirror symmetry, canonical bundle formula, the Lefschetz principle, birational transformations, and deformations of diagrams of algebras. The intention is to disseminate the knowledge of advanced results and key techniques used to solve open problems. The book is intended for all advanced graduate students and researchers interested in the new research frontiers of birational geometry and moduli spaces.

1 E. Amerik, Negative rational curves and their deformations on hyperkähler manifolds.- 2 C. Camere, Moduli spaces of cubic threefolds and of irreducible holomorphic symplectic manifolds.- 3 C. Ciliberto et al., A note on Severi varieties of nodal curves on Enriques surfaces.- 4 E. Floris and V. Lazic, A travel Guide to the canonical bundle Formula.- 5 A.-S. Kaloghiros, Some examples of Calabi-Yau pairs with maximal intersection and no toric model.- 6 E. Lepri and M. Manetti, On Deformations of diagrams of commutative Algebras.- 7 C. Lozano Huerta and A. Massarenti, The Lefschetz principle in birational geometry: birational twin variety.- 8 L. Lunardon, What is the monodromy property for degenerations of Calabi-Yau varieties?.- 9 A. Perego, Examples of irreducible symplectic varieties.- 10 A. Petracci, An example of Mirror Symmetry for Fano threefolds.- 11 S. Schreieder and L. Tasin, Chern numbers of uniruled threefolds.