Toward Clemens' Conjecture in Degrees between 10 and 24

Johnsen, Trygve, and Kleiman, Steven. "Toward Clemens' Conjecture in Degrees between 10 and 24." Serdica Mathematical Journal 23.2 (1997): 131-142. <http://eudml.org/doc/11608>.

@article{Johnsen1997,
abstract = {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.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.},
author = {Johnsen, Trygve, Kleiman, Steven},
journal = {Serdica Mathematical Journal},
keywords = {Rational Curves; Quintic Threefold; Clemens' conjecture; rational curves; quintic threefold; Hilbert scheme},
language = {eng},
number = {2},
pages = {131-142},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Toward Clemens' Conjecture in Degrees between 10 and 24},
url = {http://eudml.org/doc/11608},
volume = {23},
year = {1997},
}

TY - JOUR
AU - Johnsen, Trygve
AU - Kleiman, Steven
TI - Toward Clemens' Conjecture in Degrees between 10 and 24
JO - Serdica Mathematical Journal
PY - 1997
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 23
IS - 2
SP - 131
EP - 142
AB - 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.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.
LA - eng
KW - Rational Curves; Quintic Threefold; Clemens' conjecture; rational curves; quintic threefold; Hilbert scheme
UR - http://eudml.org/doc/11608
ER -