The Sp3-grassmannian and duality for prime Fano threefolds of genus 9

Details The Sp3-grassmannian and duality for prime Fano threefolds of genus 9 The Sp3-grassmannian and duality for prime Fano threefolds of genus 9

2002-09-16

arxiv.org/abs/math/0209197v2

Mathematics

Algebraic Geometry

20 pages, Latex

Scientific paper

By a result of Mukai, the non-abelian Brill-Noether locus X = M_C(2,K:3F) of type II, defined by a stable rank 2 vector bundle F of invariant 3 over a plane quartic curve C, is a prime Fano 3-fold X of degree 16. The associate ruled surface S^X = P(F) is uniquely defined by X, and we see that for the general X = X_{16}, S^X is isomorphic to the Fano surface of conics on X. The argument uses the geometry of the Sp_3-grassmannian and the double projection from a line on X_{16}.

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