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Surfaces in P4 with extremal general hyperplane section

✍ Scribed by Nadia Chiarli; Silvio Greco; Uwe Nagel

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
192 KB
Volume
257
Category
Article
ISSN
0021-8693

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✦ Synopsis

Optimal upper bounds for the cohomology groups of space curves have been derived recently. Curves attaining all these bounds are called extremal curves. This note is a step to analyze the corresponding problems for surfaces. We state optimal upper bounds for the second and third cohomology groups of surfaces in P 4 and show that surfaces attaining all these bounds exist and must have an extremal curve as general hyperplane section. Surprisingly, all the first cohomology groups of such surfaces vanish. It follows that an extremal curve does not lift to a locally Cohen-Macaulay surface unless the curve is arithmetically Cohen-Macaulay.

πŸ“œ SIMILAR VOLUMES

A note on threefolds with a hyperplane s
A note on threefolds with a hyperplane section of general type
✍ M. A. Cataldo; M. Palleschi πŸ“‚ Article πŸ“… 1996 πŸ› Springer 🌐 English βš– 586 KB

This paper deals with polarized pairs (Jr, L), where 3~ is a nonsingular projective threefold and L is a very ample line bundle on it, such that for one smooth member.4 E ILl, one has x(\_4) = 2. A large class of pairs whose adjoint line bundle is nef and big was indirectedly studied by Beltrametti