Abstract:We prove that a complete intersection of c very general hypersurfaces of degrees d1, . . . , dc ≥ 2 in N -dimensional complex projective space is not ruled (and therefore not rational) provided that c i=1 di ≥ 2 3 N + c + 1. To this end we consider a degeneration to positive characteristic, following Kollár. Our argument does not require a resolution of the singularities of the special fiber of the degeneration. It relies on a generalization of Kollár's "algebraic Morse lemma" that controls the dimensions of t… Show more
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