Smooth Enriques surfaces in P4 and exceptional bundles.
We consider the k-osculating varietiesOk,d to the Veronese d?uple embeddings of P2. By studying the Hilbert function of certain zero-dimensional schemes Y ⊂ P2, we find the dimension of Osk,d, the (s?1)th secant varieties of Ok,d, for 3 ≤ s ≤ 6 and s = 9, and we determine whether those secant varieties are defective or not.
This paper is part of the author's thesis, recently presented, where the following problem is treated: Characterizing the tangent cone and the equimultiple locus of a Puiseux surface (that is, an algebroid embedded surface admitting an equation whose roots are Puiseux power series) , using a set of exponents appearing in a root of an equation. The aim is knowing to which extent the well known results for the quasi-ordinary case can be extended to this much wider family.