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Scalar Flat Kähler Metrics on Affine Bundles over CP1?
"... Abstract. We show that the total space of any affine Cbundle over CP1 with negative degree admits an ALE scalarflat Kähler metric. Here the degree of an affine bundle means the negative of the selfintersection number of the section at infinity in a natural compactification of the bundle, and so ..."
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Abstract. We show that the total space of any affine Cbundle over CP1 with negative degree admits an ALE scalarflat Kähler metric. Here the degree of an affine bundle means the negative of the selfintersection number of the section at infinity in a natural compactification of the bundle, and so for line bundles it agrees with the usual notion of the degree. Key words: scalarflat Kähler metric; affine bundle; twistor space 2010 Mathematics Subject Classification: 53A30 1
Infinite transitivity on affine varieties
 In: Birational Geometry, Rational Curves, and
, 2013
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EXAMPLES OF CYLINDRICAL FANO FOURFOLDS
"... Abstract. We construct 4 different families of smooth Fano fourfolds with Picard rank 1, which contain cylinders, i.e., Zariski open subsets of the form Z × A1, where Z is a quasiprojective variety. The affine cones over such a fourfold admit effective Gaactions. Similar constructions of cylindrica ..."
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Abstract. We construct 4 different families of smooth Fano fourfolds with Picard rank 1, which contain cylinders, i.e., Zariski open subsets of the form Z × A1, where Z is a quasiprojective variety. The affine cones over such a fourfold admit effective Gaactions. Similar constructions of cylindrical Fano threefolds were done previously in [KPZ11, KPZ14a].