ENRIQUES SURFACES AND OTHER NON-PFAFFIAN SUBCANONICAL SUBSCHEMES OF CODIMENSION 3
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by David Eisenbud, Sorin Popescu, Charles Walter
http://www.math.columbia.edu/~psorin/eprints/nonpfaff.ps
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Abstract:
Abstract. We give examples of subcanonical subvarieties of codimension 3 in projective n-space which are not Pfaan, i.e. dened by the ideal sheaf of submaximal Pfaans 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 n are Pfaan, but he left open the question whether the exceptional non-Pfaan cases actually occur. We give non-Pfaan examples of the principal types allowed by his theorem, including (Enriques) surfaces in P 5 in characteristic 2 and
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