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

被引:0
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作者
Atanas Iliev
机构
[1] Bulgarian Academy of Sciences,Institute of Mathematics
来源
manuscripta mathematica | 2003年 / 112卷
关键词
Vector Bundle; Stable Rank; Fano Threefolds; Quartic Curve; Fano Surface;
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摘要
By a result of Mukai, the non-abelian Brill-Noether locus X=MC(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=X16 of degree 16. The associate ruled surface SX=P(F) is uniquely defined by X, and we see that for the general X=X16, SX is isomorphic to the Fano surface of conics on X. The argument uses the geometry of the Sp3-grassmannian and the double projection from a line on X16.
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页码:29 / 53
页数:24
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