# Toward Clemens' Conjecture in Degrees between 10 and 24

Johnsen, Trygve; Kleiman, Steven

Serdica Mathematical Journal (1997)

- Volume: 23, Issue: 2, page 131-142
- ISSN: 1310-6600

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topJohnsen, 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 -

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