2019
DOI: 10.48550/arxiv.1910.08256
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Smoothing pairs over degenerate Calabi-Yau varieties

Kwokwai Chan,
Ziming Nikolas Ma

Abstract: We apply the techniques developed in [2] to study deformations of a pair (X, C * ), where C * is a bounded perfect complex of locally free sheaves on a degenerate Calabi-Yau variety X which is a toroidal crossing space. Applying the results in [6], we prove that the pair (X, C * ) is smoothable under the assumption that H 2 (HomO X (C * , C * )0) = 0.

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Cited by 1 publication
(5 citation statements)
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“…By applying Serre duality and the main result (Corollary 4.7) of [2], we obtain the following corollary Corollary 1.3 (=Corollary 6.6). If L n is simple, then the pair ( X0 ( B, P, š), E 0 (L n )) is smoothable.…”
Section: Introductionmentioning
confidence: 85%
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“…By applying Serre duality and the main result (Corollary 4.7) of [2], we obtain the following corollary Corollary 1.3 (=Corollary 6.6). If L n is simple, then the pair ( X0 ( B, P, š), E 0 (L n )) is smoothable.…”
Section: Introductionmentioning
confidence: 85%
“…With a choice of gluing data š, by the main theorem of [12], both X0 (B, P, š) and X0 ( B, P, š) are smoothable to toric degenerations p : X → S, p : X → S over S := Spec(C[[t]]), respectively. Next, we want to apply the main result (Corollary 4.7) in [2]. Therefore, we need to compute the cohomology group H 2 ( X0 ( B, P, š), End 0 (E 0 (L m,n ))).…”
Section: Simplicity and Smoothingmentioning
confidence: 99%
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