The enumerative geometry of rational and elliptic curves in projective space

@article{Vakil1997TheEG,
  title={The enumerative geometry of rational and elliptic curves in projective space},
  author={R. Vakil},
  journal={arXiv: Algebraic Geometry},
  year={1997}
}
  • R. Vakil
  • Published 1997
  • Mathematics
  • arXiv: Algebraic Geometry
We study the geometry of varieties parametrizing degree d rational and elliptic curves in P^n intersecting fixed general linear spaces and tangent to a fixed hyperplane H with fixed multiplicities along fixed general linear subspaces of H. As an application, we derive recursive formulas for the number of such curves when the number is finite. These recursive formulas require as ``seed data'' only one input: there is one line in P^1 through two points. These numbers can be seen as top… Expand
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