On normal surface singularities and a problem of enriques |
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Authors: | C Ciliberto S Greco |
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Institution: | 1. Dipartmento Di Matematica , Università Di Tor Vergnta , Via Della Ricerca Scientifica, 1-00133, Roma E-mail: CILIBERTOaxp. mat. utovrm. it;2. Politecnico Di Torino Dipartmento Di Matematica , Corso Duca Degli Abruzzi 24, Torino, 10129, Italy E-mail: SGREC0QP0LIT0. IT |
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Abstract: | We construct families of normal surface singularities with the following property: given any fiat projective connected family V →B of smooth, irreducible, minimal algebraic surfaces, the general singularity in one of our families cannot occur, analytically, on any algebraic surfaces which is Irrationally equivalent to a surface in V→B. In particular this holds for V→B consisting of a single rational surface, thus answering negatively to a long standing problem posed by F. Enriques. In order to prove the above mentioned results, wo develop a general, though elementary, method, based on the consideration of suitable correspondences, for comparing a given family of minimal surfaces with a family of surface singularities. Specifically the method in question gives us the possibility of comparing the parameters on which the two families depend, thus leading to the aforementioned results. |
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Keywords: | 14J17 32S05 |
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