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- W2035369300 abstract "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 P4 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." @default.
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- W2035369300 date "2002-11-01" @default.
- W2035369300 modified "2023-09-30" @default.
- W2035369300 title "Surfaces in P4 with extremal general hyperplane section" @default.
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- W2035369300 doi "https://doi.org/10.1016/s0021-8693(02)00121-7" @default.
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