Proof of a conjecture of Batyrev and Nill

Favero, David; Kelly, Tyler L.

doi:10.1353/ajm.2017.0038

Cited by 12 publications

(22 citation statements)

References 18 publications

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“…For example, the Batyrev-Nill conjecture, Conjecture 5.3 of [BN07], is just Case (c) of Corollary 5.15. This recovers the main result of [FK14]. As an instructive example, we specialize to the case of Orlov's theorem on the fan associated to the line bundle tot(O P n (−d)), which we do as an example in Subsection 6.1.…”

Section: Introductionsupporting

confidence: 63%

“…Such a description was given by Mavlyutov (Lemma 1.6 of [Mav09]) for the case when i D i = −K X Σ . In [FK14], this hypothesis is dropped:…”

Section: Toric Landau-ginzburg Models: Their Cones and Phasesmentioning

confidence: 99%

“…We can break the above proposition into the following two lemmas. These are already implicit in the proof of Propoisition 5.16 of [FK14] but we include them here for completeness.…”

Section: Toric Landau-ginzburg Models: Their Cones and Phasesmentioning

confidence: 99%

“…Lemma 4.6 (Lemma 5.17 of[FK14]). Let Σ be a complete fan andD i = ρ a iρ D ρbe nef and Q-Cartier divisors.…”

mentioning

confidence: 99%

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Fractional Calabi�Yau categories from Landau�Ginzburg models

Favero¹

2018

Alg. Geom.

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We give criteria for the existence of a Serre functor on the derived category of a gauged Landau-Ginzburg model. This is used to provide a general theorem on the existence of an admissible (fractional) Calabi-Yau subcategory of a gauged Landau-Ginzburg model and a geometric context for crepant categorical resolutions. We explicitly describe our framework in the toric setting. As a consequence, we generalize several theorems and examples of Orlov and Kuznetsov, ending with new examples of semi-orthogonal decompositions containing (fractional) Calabi-Yau categories. S = − ⊗ ω X [n].

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Section: Introductionsupporting

confidence: 63%

“…Such a description was given by Mavlyutov (Lemma 1.6 of [Mav09]) for the case when i D i = −K X Σ . In [FK14], this hypothesis is dropped:…”

Section: Toric Landau-ginzburg Models: Their Cones and Phasesmentioning

confidence: 99%

“…We can break the above proposition into the following two lemmas. These are already implicit in the proof of Propoisition 5.16 of [FK14] but we include them here for completeness.…”

Section: Toric Landau-ginzburg Models: Their Cones and Phasesmentioning

confidence: 99%

“…Lemma 4.6 (Lemma 5.17 of[FK14]). Let Σ be a complete fan andD i = ρ a iρ D ρbe nef and Q-Cartier divisors.…”

mentioning

confidence: 99%

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Fractional Calabi�Yau categories from Landau�Ginzburg models

Favero¹

2018

Alg. Geom.

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“…We can describe our birational Calabi-Yau threefolds in this general setting. See references [7,12] for recent works which shed light on this general phenomenon from the derived categories of Calabi-Yau threefolds.…”

Section: Cones For Complete Intersections and Calabi-yau Manifoldsmentioning

confidence: 99%

Movable vs Monodromy Nilpotent Cones of Calabi-Yau Manifolds

Hosono¹,

Takagi²

2018

SIGMA

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Homological mirror symmetry for generalized Greene–Plesser mirrors

Sheridan

Smith

2020

Invent. math.

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We prove Kontsevich’s homological mirror symmetry conjecture for certain mirror pairs arising from Batyrev–Borisov’s ‘dual reflexive Gorenstein cones’ construction. In particular we prove HMS for all Greene–Plesser mirror pairs (i.e., Calabi–Yau hypersurfaces in quotients of weighted projective spaces). We also prove it for certain mirror Calabi–Yau complete intersections arising from Borisov’s construction via dual nef partitions, and also for certain Calabi–Yau complete intersections which do not have a Calabi–Yau mirror, but instead are mirror to a Calabi–Yau subcategory of the derived category of a higher-dimensional Fano variety. The latter case encompasses Kuznetsov’s ‘K3 category of a cubic fourfold’, which is mirror to an honest K3 surface; and also the analogous category for a quotient of a cubic sevenfold by an order-3 symmetry, which is mirror to a rigid Calabi–Yau threefold.

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Proof of a conjecture of Batyrev and Nill

Cited by 12 publications

References 18 publications

Fractional Calabi�Yau categories from Landau�Ginzburg models

Fractional Calabi�Yau categories from Landau�Ginzburg models

Movable vs Monodromy Nilpotent Cones of Calabi-Yau Manifolds

Homological mirror symmetry for generalized Greene–Plesser mirrors

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