Global smoothing of Calabi-Yau threefolds

Namikawa, Yoshinori; Steenbrink, J. H. M.

doi:10.1007/bf01231450

Cited by 65 publications

(82 citation statements)

References 21 publications

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“…-We only treat the case dim X = 3, the surface case being easier and left to the reader. By [22],X admits a finite étale cover h : X →X which is birational to a product of a simply connected manifold and an abelian variety. By our assumption on the universal cover, the simply connected part does not appear.…”

Section: The Universal Covermentioning

confidence: 99%

Geometric stability of the cotangent bundle and the universal cover of a projective manifold

Campana¹,

Peternell²

2011

Bul. Soc. Math. France

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Abstract. -We first prove a strengthening of Miyaoka's generic semi-positivity theorem: the quotients of the tensor powers of the cotangent bundle of a non-uniruled complex projective manifold X have a pseudo-effective (instead of generically nef) determinant. A first consequence is that X is of general type if its cotangent bundle contains a subsheaf with 'big' determinant. Among other applications, we deduce that if the universal cover of X is not covered by compact positive-dimensional analytic subsets, then X is of general type if χ(O X ) = 0. We finally show that if L is a numerically trivial line bundle on X, and if K X + L is Q-effective, then so is K X itself. The proof of this result rests on Simpson's work on jumping loci of numerically trivial line bundles, and Viehweg's cyclic covers. This last result is central, and has been recently extended, using the very same ingredients, to the case of log-canonical pairs. cotangent a un sous-faisceau dont le déterminant est 'big'. Parmi diverses applications, nous montrons que si le revêtement universel de X n'est pas recouvert par des sousensembles analytiques compacts de dimension strictement positive, alors X est de type général si χ(O X ) = 0.Nous montrons enfin que K X est Q-effectif si K X + L l'est, pour un fibré en droites numériqiuement effectif L sur X. La démonstration de ce résultat central repose sur les travaux de C. Simpson sur les lieux de Green-Lazarsfeld, et sur les revêtements cycliques de Viehweg. Ce résultat a été récemment étendu aux paires 'Log-canoniques' en utilisant les mêmes ingrédients.

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Section: The Universal Covermentioning

confidence: 99%

Geometric stability of the cotangent bundle and the universal cover of a projective manifold

Campana¹,

Peternell²

2011

Bul. Soc. Math. France

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“…This fact characterizes the global change in topology induced by a conifold transition, as explained in the following [62], [74], [71], [55], [52], ..…”

Section: Again Bott Formulas (22) and Calabi-yau Condition Imply Thatmentioning

confidence: 99%

“…In section 3 the global change in topology induced by a conifold transition is carefully studied, relying each other homological invariants of all of the three poles of a conifold transition (theorem 3.2). This section ends up with some similar considerations for more general geometric transitions, essentially due to Y. Namihawa and J. Steenbrimk [55]. Section 4 gives an outline of results and technics needed to perform a (actually incomplete) classification of geometric transition.…”

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confidence: 99%

Geometric transitions

Rossi

2006

Journal of Geometry and Physics

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“…If the answer to the question is positive, then the first proof of smoothability of Q-factorial Calabi-Yau threefolds from [10] goes through if these have isolated complete intersection singularities.…”

Section: -^ H^y^loge^-e)) -^ T^ - Hi(y^y{\og E)(-e)) -^mentioning

confidence: 99%

“…In [9], the second proof of [10] is generalized even further: Namikawa there admits smoothable isolated singularities which are either toric or have smooth semiuniversal base space.…”

Section: -^ H^y^loge^-e)) -^ T^ - Hi(y^y{\og E)(-e)) -^mentioning

confidence: 99%

Du Bois invariants of isolated complete intersection singularities

Steenbrink¹

1997

Annales De L’institut Fourier

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Global smoothing of Calabi-Yau threefolds

Cited by 65 publications

References 21 publications

Geometric stability of the cotangent bundle and the universal cover of a projective manifold

Geometric stability of the cotangent bundle and the universal cover of a projective manifold

Geometric transitions

Du Bois invariants of isolated complete intersection singularities

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