Two components of the boundary of the compactification of the variety of instantons

Details Two components of the boundary of the compactification of the variety of instantons Two components of the boundary of the compactification of the variety of instantons

1999-01-05

arxiv.org/abs/math/9901011v2

Mathematics

Algebraic Geometry

In french. This is a completely revisited version with many improvements in the proofs

Scientific paper

We study two components of the boundary of the compactification of the variety I_3 of instantons of degree three. We use the desciption of I_3 as symetric (involutive) cubo-cubic transforms deduced from the Beilinson monade. It involves some geometry of curves and surfaces in P^3. This allows us to distinguish two irreducible components which are in the closure of involutive cubo-cubic transforms. It gives us two irreducible components of the boundary of I_3. Moreover, we show that the cubo-cubic transforms of one of these components are the inverse of the other one.

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