Rational curves on general type hypersurfaces
نویسندگان
چکیده
منابع مشابه
Rational 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.
متن کاملRational Curves on Hypersurfaces of Low Degree Ii
This is the second in a sequence of papers on the geometry of spaces of rational curves of degree e on a general hypersurface X ⊂ Pn of degree d. In [11] it is proved that if d < n+1 2 then for each e the space of rational curves is irreducible, reduced and has the expected dimension. In this paper it is proved that if d2 + d + 1 ≤ n, then for each e the space of rational curves is a rationally...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2020
ISSN: 0022-040X
DOI: 10.4310/jdg/1603936816