Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 44, No. 1, pp. 111-126 (2003)

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Projective Schemes with Degenerate General Hyperplane Section II

E. Ballico, N. Chiarli and S. Greco

Dipartimento di Matematica Università di Trento, 38050 Povo (TN), Italy; Dipartimento di Matematica Politecnico di Torino 10129 Torino, Italy; e-mail:; e-mail:; e-mail:

Abstract: We study projective non-degenerate closed subschemes $X \subseteq {\bf P}^n$ having degenerate general hyperplane section, continuing our earlier work. We find inequalities involving three relevant integers, namely: the dimensions of the spans of $X_{red}$ and of the general hyperplane section of $X$, and a measure of the ``fatness'' of $X$, which is introduced in this paper. We prove our results first for curves and then for higher dimensional schemes by induction, via hyperplane sections. All our proofs and results are characteristic free. We add also many clarifying examples.

Classification (MSC2000): 14H50, 14N05; 14M99

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Electronic version published on: 3 Apr 2003. This page was last modified: 4 May 2006.

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