Curves in the double plane |
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| Authors: | Robin Hartshorne Enrico Schlesinger |
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| Affiliation: | 1. Department Of Mathematics , University Of California , Berkeley, CA, 94720, U S A E-mail: robinqmath.berkeley.edu;2. Dlpartimento di matematicà , Universitá degli studi di trento , vla Sommarive, Povo(tento), 38050, Italia E-mail: enrschQmate.polimi. it |
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| Abstract: | We study in detail locally Cohen-Macaulay curves in P4 which are contained in a double plane 2H, thus completing the classification of curves lying on surfaces of degree two. We describe the irreducible components of the Hilbert schemes H d,g(2H) of lo-cally Cohen-Macaulay curves in 2H of degree d and arithmetic genus g, and we show that H d,g(2H) is connected. We also discuss the Rao module of these curves and liaison and biliaison equiva-lence classes. |
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| Keywords: | 14H10 14H50 14C50 |
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