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摘要
We prove that the space of smooth rational curves of degree e on a general complete intersection of multidegree (d(1), ... , d(m)) in P-n is irreducible of the expected dimension if Sigma(m)(i=1) d(i) < (2n + m + 1)/3 and n is sufficiently large. This generalizes a result of Harris, Roth and Starr [Rational curves on hypersurfaces of low degree, J. Reine Angew. Math. 571 (2004), 73-106], and is achieved by proving that the space of conics passing through any point of a general complete intersection has constant dimension if Sigma(m)(i=1) d(i) is small compared to n.
- 出版日期2013-6
