منابع مشابه
Generators for Vector Bundles on Generic Hypersurfaces
We prove that on a generic hypersurface in P of dimension at least 3, a vector bundle with r ≤ m generators must be split if m is odd. If m is even, then the same is true if the degree of X is at least 3.
متن کاملRational Curves on Smooth Cubic Hypersurfaces
We prove that the space of rational curves of a fixed degree on any smooth cubic hypersurface of dimension at least four is irreducible and of the expected dimension. Our methods also show that the space of rational curves of a fixed degree on a general hypersurface in Pn of degree 2d ≤ min(n+4, 2n−2) and dimension at least three is irreducible and of the expected dimension.
متن کاملLooking for Rational Curves on Cubic Hypersurfaces
The aim of these lectures is to study rational points and rational curves on varieties, mainly over finite fields Fq. We concentrate on hypersurfaces Xn of degree ≤ n+ 1 in Pn+1, especially on cubic hypersurfaces. The theorem of Chevalley–Warning (cf. Esnault’s lectures) guarantees rational points on low degree hypersurfaces over finite fields. That is, if X ⊂ Pn+1 is a hypersurface of degree ≤...
متن کاملRational Curves on Hypersurfaces (after A. Givental)
We describe here a remarkable relationship studied by Givental between hypergeometric series and the quantum cohomology of hypersurfaces in pro-jective space [G1]. As the quantum product involves genus 0 Gromov-Witten invariants, a connection between hypergeometric series and the geometry of rational curves on the hypersurfaces is made. While the most general context for such relationships has ...
متن کاملRational Curves on Smooth Cubic Hypersurfaces over Finite Fields
Let k be a finite field with characteristic exceeding 3. We prove that the space of rational curves of fixed degree on any smooth cubic hypersurface over k with dimension at least 11 is irreducible and of the expected dimension.
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 1986
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.1521