Deforming Calabi-Yau Threefolds

Abstract

This paper first generalises the Bogomolov-Tian-Todorov unobstructedness theorem to the case of Calabi-Yau threefolds with canonical singularities. The deformation space of such a Calabi-Yau threefold is no longer smooth, but the general principle is that the obstructions to deforming such a threefold are precisely the obstructions to deforming the singularities of the threefold. Secondly, these results are applied to smoothing singular Calabi-Yau threefolds with crepant resolutions. Any such Calabi-Yau threefold with isolated complete intersection singularities which are not ordinary double points is smoothable. A Calabi-Yau threefold with non-complete intersection isolated singularities is proved to be smoothable under much stronger hypotheses.

Post-publication revision, correcting one error and clarifying an aspect of the proof of Theorem 2.2

References in corpus (1)

• Primitive Calabi-Yau Threefolds

Cited by in corpus (19)

• Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
• Asymptotically conical Calabi-Yau manifolds, I
• Geometric Transitions
• Dynamic SU(2) Structure from Seven-branes
• Primitive contractions of Calabi-Yau threefolds II
• Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds I
• Non-Spherical Horizons, I
• The 14th case VHS via K3 fibrations
• Homological Type of Geometric Transitions
• Primitive Calabi-Yau Threefolds
• Large N dualities and transitions in geometry
• Cubic Extremal Transition and Gromov-Witten Theory
• Flops and Poisson deformations of symplectic varieties
• Del Pezzo singularities and SUSY breaking
• On the connectedness of the standard web of Calabi-Yau 3-folds and small transitions
• Gromov-Witten theory under degree-4 Type II Extremal Transitions
• Analytic equivalence of geometric transitions
• Deformations of weak Fano 3-folds with only terminal singularities
• Flips from 4-folds with isolated complete intersection singularities whose downstairs have rational bi-elephants