Calabi-Yau manifolds with large Picard number

Wilson, P. Μ. H.

doi:10.1007/bf01388848

Cited by 46 publications

(55 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The lack of understanding of Calabi-Yau threefolds is the main gap in the classification of 3-dimensional algebraic varieties (see [Wi1], [Wi2], [Wi3], [N2], [Gr2]). For various reasons manifolds with Picard group of rank 1 play a special role among all Calabi-Yau threefolds (see [Gr2], [ES], [R1], [L2], [KN], [L1], [Be]).…”

Section: Introductionmentioning

confidence: 99%

Primitive contractions of Calabi-Yau threefolds II

Kapustka

2008

Journal of the London Mathematical Society

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Primitive contractions of Calabi-Yau threefolds II

Kapustka

2008

Journal of the London Mathematical Society

View full text Add to dashboard Cite

show abstract

“…Throughout this section, X is assumed to be a Calabi-Yau threefold with C2(X) > 0. According to [24,17,26], every possible proper fiber space structure tp : X -> W is one of the following: Case 1. W = P 1 and the general fiber is a K3 surface; Case 2, ip is an elliptic fibration with Aw > 0.…”

Section: Claim (25) There Is An Effective Cartier Divisor E Supportmentioning

confidence: 99%

“…Then there are only finitely many proper algebraic fiber structures on X of the form $p| : X -► W with D-C2{X)>eD-H 2 (cf. [24]). …”

Section: C2(x) • Ip*(h) = C2(-y) • M < 12 + 12smentioning

confidence: 99%

See 1 more Smart Citation

Calabi–Yau threefolds with positive second Chern class

Oguiso¹,

Peternell²

1998

Communications in Analysis and Geometry

View full text Add to dashboard Cite

G Aut(X) covers the convex hull of the rational points lying in the nef cone Amp(X).However, at the present time, this conjecture has been checked only for one non-trivial example by [7] and very little are known in general.On the other hand, in the course of his classification program of CalabiYau threefolds according to the behaviour of the second Chern class, Wilson ([26]) observed that the automorphism group of a Calabi-Yau threefold X, which is in general a discrete group, is actually finite if the second Chern class is positive, that is, C2(X) • D > 0 for all non-zero nef divisors D, and then asked : Question 1. Is the nef cone of a Calabi-Yau threefold with positive second Chern class a finite rational polyhedral cone?

show abstract

“…These varieties have been studied by the second author in the series of papers [10,11,12]. These varieties have been studied by the second author in the series of papers [10,11,12].…”

Section: Introductionmentioning

confidence: 99%