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Rational curves on Del Pezzo manifolds

Rational curves on Del Pezzo manifolds AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Geometry de Gruyter

Rational curves on Del Pezzo manifolds

Zahariuc, Adrian
Advances in Geometry , Volume 18 (4): 15 – Oct 25, 2018
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15 pages

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Publisher
de Gruyter
Copyright
© 2018 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1615-7168
eISSN
1615-7168
DOI
10.1515/advgeom-2018-0010
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Advances in Geometry – de Gruyter

Published: Oct 25, 2018

References

  • Pencils of quadrics and Gromov–Witten–Welschinger invariants of ℂP3
  • Anticanonical models of three-dimensional algebraic varieties
  • Normal bundles of rational curves in projective spaces
  • The quantum cohomology of blow-ups of ℙ2 and enumerative geometry
  • On the normal bundles of smooth rational space curves
  • Normal bundles of rational curves in projective spaces