## Topics in the geometry of projective space: recent work of F.L. Zak |

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Topics in the Geometry of Projective Space: Recent Work of F.L. Zak Robert Lazarsfekd,Ven Limited preview - 2012 |

### Common terms and phrases

2-plane algebraic groups birational bivectors of rank Borel subgroup classification theorem codimension complete intersection connectedness theorem contains cubic hypersurface defined denotes dimension n/2 dimensional embedding exists a point F e Sec(A follows four standard Grassmannian Hartshorne varieties Hartshorne's conjecture Hence highest weight vector hyperplane section IP1 x IP3 irreducible representations isomorphism linear normality linear space linear subspaces linear system obtain orbits of dimensions parabolic subgroup parametrized plane point F primitive element projective bundle projective space projective variety punctured cone QP meeting quadratic equations quadric of dimension resolution of singularities Schubert cycles secant deficiency secant quadric QP secant variety singular smooth projective variety smooth quadric spinor variety subvarieties suffices to show system of quadrics tangent space Terracini's lemma Theorem 2.1 theorem on tangencies three orbits variety corresponding variety of dimension verify Zak's classification Zak's proof Zak's theorem