Enriques Surfaces and other Non-Pfaffian Subcanonical Subschemes of Codimension 3

Enriques Surfaces and Other Non-pfaffian Subcanonical Subschemes of Codimension

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We give examples of subcanonical subvarieties of codimension 3 in projective n-space which are not Pfaffian, i.e. defined by the ideal sheaf of submaximal Pfaffians of an alternating map of vector bundles. This gives a negative answer to a question asked by Okonek [29]. Walter [36] had previously shown that a very large majority of subcanonical subschemes of codimension 3 in P are Pfaffian, but...

Lagrangian Subbundles and Codimension 3 Subcanonical Subschemes

We show that a Gorenstein subcanonical codimension 3 subscheme Z ⊂ X = P , N ≥ 4, can be realized as the locus along which two Lagrangian subbundles of a twisted orthogonal bundle meet degenerately, and conversely. We extend this result to singular Z and all quasiprojective ambient schemes X under the necessary hypothesis that Z is strongly subcanonical in a sense defined below. A central point...

Construction of Calabi-yau 3-folds in P 6

We announce here the construction of examples of smooth Calabi-Yau 3-folds in P6 of low degree, up to degree 17. In the last degree their construction is rather complicated, and parametrized by smooth septics in P2 having a a g1 d with d = 13, 12, or 10. This turns out to show the existence of three unirational components of their Hilbert scheme, all having the same dimension 23+ 48 = 71. The c...

Quadratic Sheaves and Self – Linkage

The present paper is devoted to the proof of a structure theorem for self–linked pure subschemes C ⊆ P n k of codimension 2 over a field k of characteristic p = 2. We use the symbol C because the classical case to be studied was the one of reduced curves in P 3 k. In this case, one can describe the notion of self–linkage in non–technical terms, saying that C is self–linked if and only if there ...