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Curves of degree r + 2 in ℙr: Cohomological, geometric, and homological aspects


Brodmann, M; Schenzel, P (2001). Curves of degree r + 2 in ℙr: Cohomological, geometric, and homological aspects. Journal of Algebra, 242(2):577-623.

Abstract

Let C⊆Prk be a non-degenerate projective curve of degree r+2, where r≥3. By means of the Hartshorne-Rao module of C we distinguish 4 different possible cases (and an exceptional case which only appears if r=3). In any case C is obtained either by means of an embedding of an arbitrary smooth curve C0 of genus 2, or by projecting an elliptic normal curve from a point or by projecting a rational normal curve from a line. Finally, the possible minimal free resolutions of the homogeneous coordinate ring of C are studied. © 2001 Academic Press.

Abstract

Let C⊆Prk be a non-degenerate projective curve of degree r+2, where r≥3. By means of the Hartshorne-Rao module of C we distinguish 4 different possible cases (and an exceptional case which only appears if r=3). In any case C is obtained either by means of an embedding of an arbitrary smooth curve C0 of genus 2, or by projecting an elliptic normal curve from a point or by projecting a rational normal curve from a line. Finally, the possible minimal free resolutions of the homogeneous coordinate ring of C are studied. © 2001 Academic Press.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Betti numbers; Castelnuovo regularity; Elliptic normal curve; Hartshorne-Rao module; Projective curves; Rational normal curve; Surface of minimal degree
Language:English
Date:2001
Deposited On:27 May 2010 16:29
Last Modified:05 Apr 2016 13:25
Publisher:Elsevier
ISSN:0021-8693
Publisher DOI:https://doi.org/10.1006/jabr.2001.8847
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1031.14013

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