On rational varieties of small rationality degree
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Davide Fusi
Abstract
We prove a stronger version of a criterion of rationality given by Ionescu and Russo. We use this stronger version to define an invariant for rational varieties (we call it rationality degree), and we classify rational varieties for small values of the invariant.
Acknowledgements
I am extremely grateful to my PhD advisor, T. de Fernex, for proposing the problem to me, for his useful comments, suggestions and support. I would also like to thank the referee for the valuable comments to the first version of this manuscript.
References
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- On the umbilicity of generalized linear Weingarten hypersurfaces in hyperbolic spaces
- Regular polyhedra in the 3-torus
- Rational curves on Del Pezzo manifolds
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- On rational varieties of small rationality degree
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Articles in the same Issue
- Frontmatter
- The index of symmetry of three-dimensional Lie groups with a left-invariant metric
- Canonical contact unit cotangent bundle
- On the umbilicity of generalized linear Weingarten hypersurfaces in hyperbolic spaces
- Regular polyhedra in the 3-torus
- Rational curves on Del Pezzo manifolds
- Commuting matrices and the Hilbert scheme of points on affine spaces
- On rational varieties of small rationality degree
- Skew symmetric logarithms and geodesics on On(ℝ)
- New homogeneous Einstein metrics on quaternionic Stiefel manifolds
