TY - JOUR
T1 - Curves disjoint from a nef divisor
AU - Lesieutre, John
AU - Ottem, John Christian
N1 - Publisher Copyright:
© 2016, University of Michigan. All rights reserved.
PY - 2016/6
Y1 - 2016/6
N2 - On a projective surface it is well known that the set of curves orthogonal to a nef line bundle is either finite or uncountable. We show that this dichotomy fails in higher dimension by constructing an effective, nef line bundle on a threefold that is trivial on countably infinitely many curves. This answers a question of Totaro. As a pleasant corollary, we exhibit a quasi-projective variety with only a countably infinite set of complete, positive-dimensional subvarieties.
AB - On a projective surface it is well known that the set of curves orthogonal to a nef line bundle is either finite or uncountable. We show that this dichotomy fails in higher dimension by constructing an effective, nef line bundle on a threefold that is trivial on countably infinitely many curves. This answers a question of Totaro. As a pleasant corollary, we exhibit a quasi-projective variety with only a countably infinite set of complete, positive-dimensional subvarieties.
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U2 - 10.1307/mmj/1465329015
DO - 10.1307/mmj/1465329015
M3 - Article
AN - SCOPUS:84975894224
SN - 0026-2285
VL - 65
SP - 321
EP - 332
JO - Michigan Mathematical Journal
JF - Michigan Mathematical Journal
IS - 2
ER -