Canonical models of toric hypersurfaces

Batyrev, Victor V.

doi:10.14231/ag-2023-013

Cited by 3 publications

(5 citation statements)

References 23 publications

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“…We note that as was shown in [86], choosing an FRST of ∆ • corresponds to a maximal projective crepant partial desingularization (MPCP desingularization). An MPCP desingularization can completely resolve singularities of toric CY n-folds for n ≤ 3, but need not for n > 3.…”

Section: Strata Of Cy Hypersurfacesmentioning

confidence: 80%

“…In this section, following the methods of [86], we now explain how to construct a (d − 1)dimensional Calabi-Yau (CY) toric hypersurface and its stratifications from a pair of ddimensional reflexive lattice polytopes ∆, ∆ • where ∆ ⊂ M is the usual Newton polytope and its polar dual ∆ • ⊂ N is defined below [86].…”

Section: Calabi-yau Toric Hypersurfaces and Reflexive Pairsmentioning

confidence: 99%

“…A more complete discussion of possible types of singularities of toric varieties can be found in, e.g [86,92,93]16.…”

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confidence: 99%

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On the intermediate Jacobian of M5-branes

Jefferson,

Kim

2024

J. High Energ. Phys.

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We study Euclidean M5-branes wrapping vertical divisors in elliptic Calabi-Yau fourfold compactifications of M/F-theory that admit a Sen limit. We construct these Calabi-Yau fourfolds as elliptic fibrations over coordinate flip O3/O7 orientifolds of toric hypersurface Calabi-Yau threefolds. We devise a method to analyze the Hodge structure (and hence the dimension of the intermediate Jacobian) of vertical divisors in these fourfolds, using only the data available from a type IIB compactification on the O3/O7 Calabi-Yau orientifold. Our method utilizes simple combinatorial formulae (that we prove) for the equivariant Hodge numbers of the Calabi-Yau orientifolds and their prime toric divisors, along with a formula for the Euler characteristic of vertical divisors in the corresponding elliptic Calabi-Yau fourfold. Our formula for the Euler characteristic includes a conjectured correction term that accounts for the contributions of pointlike terminal ℤ2 singularities corresponding to perturbative O3-planes. We check our conjecture in a number of explicit examples and find perfect agreement with the results of direct computations.

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Section: Strata Of Cy Hypersurfacesmentioning

confidence: 80%

Section: Calabi-yau Toric Hypersurfaces and Reflexive Pairsmentioning

confidence: 99%

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On the intermediate Jacobian of M5-branes

Jefferson,

Kim

2024

J. High Energ. Phys.

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“…In this appendix we review the derivation of [27] for the quantum sheaf cohomology of ordinary flag manifolds 6 . We will obtain an equivalent but simpler form of the ring structure by using a different set of generators.…”

Section: Data Availability Statementmentioning

confidence: 99%

“…Since its appearance in the context of topological quantum field theories [1,2], quantum cohomology has drawn tremendous interest among physicists and mathematicians (see, e.g. [3,4,[6][7][8][9][10][11][12]). It is a variant of the ordinary cohomology ring of the target space, and encodes enumerative data known as Gromov-Witten invariants (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

Quantum cohomology of symplectic flag manifolds

Guo¹,

Zou²

2022

J. Phys. A: Math. Theor.

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We compute the quantum cohomology of symplectic flag manifolds. The ring structure was known in the special cases of symplectic Grassmannians and complete symplectic flag manifolds. Starting from a GLSM construction, our computation gives the ring structure of quantum cohomology for all symplectic flag manifolds. Symplectic flag manifolds can be described by non-abelian GLSMs with superpotential. Although the ring relations cannot be directly read off from the equations of motion on the Coulomb branch due to the complication introduced by the non-abelian gauge symmetry, it can be shown that they can be extracted from the localization formula in a gauge-invariant form. We show that, when restricted to symplectic Grassmannians and complete symplectic flag manifolds, our general result reduces to the previously established results derived by other means. We also explain why a (0,2) deformation of the GLSM does not give rise to a deformation of the quantum cohomology.

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Projecting Lattice Polytopes According to the Minimal Model Program

Batyrev

2024

Simons Symposia

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Canonical models of toric hypersurfaces

Cited by 3 publications

References 23 publications

On the intermediate Jacobian of M5-branes

On the intermediate Jacobian of M5-branes

Quantum cohomology of symplectic flag manifolds

Projecting Lattice Polytopes According to the Minimal Model Program

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