Hodge numbers for all CICY quotients

The quintic family must be the most studied family of Calabi‐Yau threefolds. Particularly symmetric members of this family are known to admit quotients by freely acting symmetries isomorphic to double-struckZ5×double-struckZ5. The corresponding quotient manifolds may themselves be symmetric. That is, they may admit symmetries that descend from the symmetries that the manifold enjoys before the quotient is taken. The formalism for identifying these symmetries was given a long time ago by Witten and instances of these symmetric quotients were given also, for the family double-struckP7false[2,2,2,2false], by Goodman and Witten. We rework this calculation here, with the benefit of computer assistance, and provide a complete classification. Our motivation is largely to develop methods that apply also to the analysis of quotients of other CICY manifolds, whose symmetries have been classified recently. For the double-struckZ5×double-struckZ5 quotients of the quintic family, our list contains families of smooth manifolds with symmetry Z4, Dic3 and Dic5, families of singular manifolds with four conifold points, with symmetry Z6 and Q8, and rigid manifolds, each with at least a curve of singularities, and symmetry Z10. We intend to return to the computation of the symmetries of the quotients of other CICYs elsewhere.

Section: Symmetries Of Quintic Quotients From Automorphisms Of Pmentioning

confidence: 60%

Section: Symmetries Of Quintic Quotients From Automorphisms Of Pmentioning

confidence: 60%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Highly Symmetric Quintic Quotients

Candelas

Mishra

2018

Calabi‐Yau Threefolds with Small Hodge Numbers

Candelas

Constantin

Mishra

2018

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We present a list of Calabi‐Yau threefolds known to us, and with holonomy groups that are precisely SU(3), rather than a subgroup, with small Hodge numbers, which we understand to be those manifolds with height (h1,1+h2,1)≤24. With the completion of a project to compute the Hodge numbers of free quotients of complete intersection Calabi‐Yau threefolds, most of which were computed in Refs. [] and the remainder in Ref. [], many new points have been added to the tip of the Hodge plot, updating the reviews by Davies and Candelas in Refs. []. In view of this and other recent constructions of Calabi‐Yau threefolds with small height, we have produced an updated list.

Formulae for Line Bundle Cohomology on Calabi‐Yau Threefolds

Constantin

Lukas

2019

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We present closed form expressions for the ranks of all cohomology groups of holomorphic line bundles on several Calabi-Yau threefolds realised as complete intersections in products of projective spaces. The formulae have been obtained by systematising and extrapolating concrete calculations and they have been checked computationally. Although the intermediate calculations often involve laborious computations of ranks of Leray maps in the Koszul spectral sequence, the final results for cohomology follow a simple pattern. The space of line bundles can be divided into several different regions, and in each such region the ranks of all cohomology groups can be expressed as polynomials in the line bundle integers of degree at most three. The number of regions increases and case distinctions become more complicated for manifolds with a larger Picard number. We also find explicit cohomology formulae for several non-simply connected Calabi-Yau threefolds realised as quotients by freely acting discrete symmetries. More cases may be systematically handled by machine learning algorithms.