• Corpus ID: 239049373

Linear subspaces of minimal codimension in hypersurfaces

  title={Linear subspaces of minimal codimension in hypersurfaces},
  author={David Kazhdan and Alexander Polishchuk},
Let k be a perfect field and let X ⊂ P be a hypersurface of degree d defined over k and containing a linear subspace L defined over k with codim PN L = r. We show that X contains a linear subspace L0 defined over k with codim PN L ≤ dr. We conjecture that the intersection of all linear subspaces (over k) of minimal codimension r contained in X, has codimension bounded above only in terms of r and d. We prove this when either d ≤ 3 or r ≤ 2. 
1 Citations
The set of forms with bounded strength is not closed
The strength of a homogeneous polynomial (or form) $f$ is the smallest length of an additive decomposition expressing it whose summands are reducible forms. We show that the set of forms with bounded


Instability in invariant theory
Let V be a representation of a reductive group G. A fundamental theorem in geometric invariant theory states that there are enough polynomial functions on V, which are invariant under G, to
The G-stable rank for tensors
We introduce the $G$-stable rank of a higher order tensors over perfect fields. The $G$-stable rank is related to the Hilbert-Mumford criterion for stability in Geometric Invariant Theory. We will
Instability in invariant theory, Ann
  • 1978