Rational curves on Del Pezzo manifolds
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Adrian Zahariuc
Abstract
We exploit an elementary specialization technique to study rational curves on Fano varieties of index one less than their dimension, known as del Pezzo manifolds. First, we study the splitting type of the normal bundles of the rational curves. Second, we prove a simple formula relating the number of rational curves passing through a suitable number of points in the case of threefolds and the analogous invariants for del Pezzo surfaces.
Acknowledgements
I would like to thank Erwan Brugallé, Yaim Cooper, Philip Engel, Penka Georgieva, János Kollár, Joe Harris, Quoc Ho, Anand Patel and Alex Perry for useful discussions. One chapter of the author’s doctoral thesis is based on this work.
Funding: While doing this work, I was indirectly supported by the National Science Foundation grant DMS-1308244, “Nonlinear Analysis on Sympletic, Complex Manifolds, General Relativity, and Graphs”.
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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
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
