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Title: Toward Clemens' Conjecture in Degrees between 10 and 24
Authors: Johnsen, Trygve
Kleiman, Steven
Keywords: Rational Curves
Quintic Threefold
Issue Date: 1997
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 23, No 2, (1997), 131p-142p
Abstract: We introduce and study a likely condition that implies the following form of Clemens’ conjecture in degrees d between 10 and 24: given a general quintic threefold F in complex P^4, the Hilbert scheme of rational, smooth and irreducible curves C of degree d on F is finite, nonempty, and reduced; moreover, each C is embedded in F with balanced normal sheaf O(−1) ⊕ O(−1), and in P^4 with maximal rank.
Description: 1 Supported in part by the Norwegian Research Council for Science and the Humanities. It is a pleasure for this author to thank the Department of Mathematics of the University of Sofia for organizing the remarkable conference in Zlatograd during the period August 28-September 2, 1995. It is also a pleasure to thank the M.I.T. Department of Mathematics for its hospitality from January 1 to July 31, 1993, when this work was started. 2Supported in part by NSF grant 9400918-DMS.
ISSN: 1310-6600
Appears in Collections:Volume 23 Number 2

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