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Titlebook: Automorphisms in Birational and Affine Geometry; Levico Terme, Italy, Ivan Cheltsov,Ciro Ciliberto,Mikhail Zaidenberg Conference proceeding

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Au(III) Series with ,C,N and ,N,N′ LigandsWe survey some results on the nonrationality and birational rigidity of certain hypersurfaces of Fano type. The focus is on hypersurfaces of Fano index one, but hypersurfaces of higher index are also discussed.
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Probing Gold: X-Ray Absorption SpectroscopyWe show that the Zariski closure of the set of hypersurfaces of degree . in ., where . ≥ 5, which are either not factorial or not birationally superrigid, is of codimension at least . in the parameter space.
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https://doi.org/10.1057/9781137471369This is a survey of some results on the structure and classification of normal analytic compactifications of .. Mirroring the existing literature, we especially emphasize the compactifications for which the curve at infinity is irreducible.
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https://doi.org/10.1007/978-3-319-06707-0Let . be an algebraically closed field of characteristic zero. Given a polynomial . with one place at infinity, we prove that either . is equivalent to a coordinate, or the family . has at most two rational elements. When . has two rational elements, we give a description of the singularities of these two elements.
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Del Pezzo Surfaces and Local InequalitiesI prove new local inequality for divisors on smooth surfaces, describe its applications, and compare it to a similar local inequality that is already known by experts.
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