Computing cohomology on toric varieties

Jurke, B.

doi:10.1090/pspum/085/1393

Cited by 1 publication

(2 citation statements)

References 11 publications

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“…For these geometeries then, we can compare the Hodge number pairs with those found in the literature to date: we find 319 pairs with 162 different Euler number which are not in the regular CICY list [2] and among them, 129 pairs with 24 different Euler number not present in the Kreuzer-Skarke list [29]. Further more, there are 16 geometries with new Hodge numbers not appearing elsewhere in the literature [58]. These 16 Hodge pairs are distributed in 8 different Euler numbers.…”

Section: Codimension (2 1) Spaces With Non-positive Euler Numbermentioning

confidence: 81%

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A new construction of Calabi–Yau manifolds: Generalized CICYs

et al. 2016

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We present a generalization of the complete intersection in products of projective space (CICY) construction of Calabi-Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility stems from the fact that they can be simply described in terms of a 'configuration matrix', a matrix of integers from which many of the details of the geometries can be easily extracted. The generalization we present is to allow negative integers in the configuration matrices which were previously taken to have positive semi-definite entries. This broadening of the complete intersection construction leads to a larger class of Calabi-Yau manifolds than that considered in previous work, which nevertheless enjoys much of the same degree of calculational control. These new Calabi-Yau manifolds are complete intersections in (not necessarily Fano) ambient spaces with an effective anticanonical class. We find examples with topology distinct from any that has appeared in the literature to date. The new manifolds thus obtained have many interesting features. For example, they can have smaller Hodge numbers than ordinary CICYs and lead to many examples with elliptic and K3-fibration structures relevant to F-theory and string dualities.1 Strictly speaking, configuration matrices describe an entire family of varieties and a variety is only determined once a choice has been made of its complex structure within the family. In this sense, it can be misleading to use the equality symbol in characterizing a specific variety by its configuration matrix. When no confusions arise, however, we will employ such a conventional abuse of notation.2 See Appendix A for a review of notation and tools to compute line bundle cohomology.

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Section: Codimension (2 1) Spaces With Non-positive Euler Numbermentioning

confidence: 81%

“…These examples with new Hodge number are listed in Table 13. [29] or elsewhere in the known literature [58].…”

Section: Codimension (2 1) Spaces With Non-positive Euler Numbermentioning

confidence: 99%