TY - JOUR
T1 - Hypersurfaces with too many rational curves
AU - Beheshti, Roya
N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2014/12
Y1 - 2014/12
N2 - We study smooth hypersurfaces of degree d ≥ n+1 in Pn whose spaces of smooth rational curves of low degrees are larger than expected, and show that under certain conditions, the primitive part of the middle cohomology of such hypersurfaces have non-trivial Hodge substructures. As an application, we prove that the space of lines on any smooth Fano hypersurface of degree d ≤ 8 in Pn has the expected dimension 2n - d - 3.
AB - We study smooth hypersurfaces of degree d ≥ n+1 in Pn whose spaces of smooth rational curves of low degrees are larger than expected, and show that under certain conditions, the primitive part of the middle cohomology of such hypersurfaces have non-trivial Hodge substructures. As an application, we prove that the space of lines on any smooth Fano hypersurface of degree d ≤ 8 in Pn has the expected dimension 2n - d - 3.
UR - https://www.scopus.com/pages/publications/84939891873
U2 - 10.1007/s00208-014-1024-8
DO - 10.1007/s00208-014-1024-8
M3 - Article
AN - SCOPUS:84939891873
SN - 0025-5831
VL - 360
SP - 753
EP - 768
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3-4
ER -