Abstract
R. Beheshti showed that for a smooth Fano hypersurface X of degree ⩽8 over the complex number field C, the dimension of the space of lines lying in X is equal to the expected dimension. We study the space of conics on X. In this case, if X contains some linear subvariety, then the dimension of the space can be larger than the expected dimension. In this paper, we show that for a smooth Fano hypersurface X of degree ⩽6 over C, and for an irreducible component R of the space of conics lying in X, if the 2-plane spanned by a general conic of R is not contained in X, then the dimension of R is equal to the expected dimension.
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