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 δp4 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.
|Number of pages||23|
|Journal||Journal of Algebra|
|State||Published - Nov 1 2002|
Bibliographical noteFunding Information:
E-mail addresses: email@example.com (N. Chiarli), firstname.lastname@example.org (S. Greco), email@example.com (U. Nagel). 1 Supported by GNSAGA-INDAM, MIUR and the VIGONI program of CRUI and DAAD. 2 The author was partially supported by the VIGONI program of CRUI and DAAD.
- Cohomoloy group
- Extremal curve
ASJC Scopus subject areas
- Algebra and Number Theory