Rational curves on a general heptic fourfold
The authors study rational curves on a general hypersurface \(X\) of degree \(7\), in the complex projective 5-space. It is known that \(X\) contains a finite number of lines, and the authors conjecture that these lines are the only rational curves on \(X\). The authors are able to prove that, for \(d\) between \(2\) and \(15\), there is no rational curve of degree \(d\) on \(X\). The result is proved by studying the generic initial ideal of a general hyperplane section of a rational curve. The procedure was introduced by Cotterill, for the study of rational curves on a general quintic threefold in the 4-space.
scientific article; zbMATH DE number 5658088