On the variety of linear spaces contained in a complete intersection

DOI10.1007/s002080050235zbMath0913.14015OpenAlexW2326224942MaRDI QIDQ1277282

Laurent Manivel, Olivier Debarre

Publication date: 31 May 1999

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002080050235

zbMATH Keywords

complete intersectionvanishing theoremChow groupunirationalBott's theorembundles on the Grassmannianlinear subspaces of dimension \(r\)

Mathematics Subject Classification ID

Vanishing theorems in algebraic geometry (14F17) Grassmannians, Schubert varieties, flag manifolds (14M15) Rational and unirational varieties (14M20) Parametrization (Chow and Hilbert schemes) (14C05) Complete intersections (14M10) Classical real and complex (co)homology in algebraic geometry (14F25) Fano varieties (14J45)

Related Items (35)

On Hilbert's 17th problem in low degree ⋮ EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS ⋮ A Noether-Lefschetz theorem for varieties of r-planes in complete intersections ⋮ Algebraic cycles on Fano varieties of some cubics ⋮ Fano schemes of generic intersections and machine learning ⋮ On Fano Schemes of Toric Varieties ⋮ Remarks on the \(\mathrm{CH}_2\) of cubic hypersurfaces ⋮ On the unirationality of quadric bundles ⋮ Probabilistic enumerative geometry over \(p\)-adic numbers: linear spaces on complete intersections ⋮ Upper bounds on resolvent degree via Sylvester's obliteration algorithm ⋮ Computing Galois groups of Fano problems ⋮ About arithmetic of intersections of two quadrics ⋮ Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi-Yau complete intersections ⋮ IRREDUCIBLE SYMPLECTIC 4-FOLDS NUMERICALLY EQUIVALENT TO (K3)^[2] ⋮ On Fano schemes of linear spaces of general complete intersections ⋮ Twisted cubics on singular cubic fourfolds -- on Starr's fibration ⋮ Abundance of 3-planes on real projective hypersurfaces ⋮ Gonality of curves on general hypersurfaces ⋮ On the restriction of holomorphic forms ⋮ Regular pairs of quadratic forms on odd-dimensional spaces in characteristic 2 ⋮ A note on gonality of curves on general hypersurfaces ⋮ Varieties with too many rational points ⋮ ABEL–JACOBI MAPS FOR HYPERSURFACES AND NONCOMMUTATIVE CALABI–YAU'S ⋮ Rational curves on hypersurfaces ⋮ On complete intersections containing a linear subspace ⋮ Rank 2 quasiparabolic vector bundles on \(\mathbb P^1\) and the variety of linear subspaces contained in two odd-dimensional quadrics ⋮ Varieties of planes on intersections of three quadrics ⋮ On Fano Schemes of Complete Intersections ⋮ Lines on projective hypersurfaces ⋮ aCM sheaves on the double plane ⋮ Rational curves on general projective hypersurfaces ⋮ Convex separably rationally connected complete intersections ⋮ Random fields and the enumerative geometry of lines on real and complex hypersurfaces ⋮ Fano schemes of complete intersections in toric varieties ⋮ Rationality of complete intersections of two quadrics over nonclosed fields

This page was built for publication: On the variety of linear spaces contained in a complete intersection