Built on

E. I. Buchbinder, A. Constantin, and A. Lukas, “The Moduli Space of Heterotic Line Bundle Models: a Case Study for the Tetra-Quadric,” JHEP
Original
1941
Earlier work this paper cites.
P. Candelas, A. Dale, C. Lutken, and R. Schimmrigk, “Complete Intersection Calabi-Yau Manifolds,” Nucl.Phys
1988
Earlier work this paper cites.
P. Candelas, C. A. Lutken, and R. Schimmrigk, “Complete Intersection Calabi-Yau Manifolds 2. Three Generation Manifolds,” Nucl. Phys
1988
Earlier work this paper cites.
World Scientific, 1991
T. Hübsch, Calabi-Yau Manifolds: A Bestiary for Physicists · 1991
Earlier work this paper cites.
L. B. Anderson, Y.-H. He, and A. Lukas, “Heterotic Compactification, An Algorithmic Approach,” JHEP
2007
Earlier work this paper cites.
L. B. Anderson, Y.-H. He, and A. Lukas, “Monad Bundles in Heterotic String Compactifications,” JHEP
Original
2008
Earlier work this paper cites.
R. Blumenhagen, B. Jurke, T. Rahn, and H. Roschy, “Cohomology of Line Bundles: A Computational Algorithm,” J. Math. Phys
Original
2010
Earlier work this paper cites.
T. Rahn and H. Roschy, “Cohomology of Line Bundles: Proof of the Algorithm,” J. Math. Phys
Original
2010
Earlier work this paper cites.
L. B. Anderson, J. Gray, Y.-H. He, and A. Lukas, “Exploring Positive Monad Bundles And a New Heterotic Standard Model,” JHEP
Original
2010
Earlier work this paper cites.
P. Candelas and R. Davies, “New Calabi-Yau Manifolds with Small Hodge Numbers,” Fortsch.Phys
Original
2010
Earlier work this paper cites.

Similar

L. B. Anderson, J. Gray, A. Lukas, and E. Palti, “Two Hundred Heterotic Standard Models on Smooth Calabi-Yau Threefolds,” Phys.Rev
Original
2011
Cited alongside, same era.
V. Braun, “On Free Quotients of Complete Intersection Calabi-Yau Manifolds,” JHEP
Original
2011
Cited alongside, same era.
R. Davies, “The Expanding Zoo of Calabi-Yau Threefolds,” Adv. High Energy Phys
Original
2011
Cited alongside, same era.
L. B. Anderson, J. Gray, A. Lukas, and E. Palti, “Heterotic Line Bundle Standard Models,” JHEP
Original
2012
Cited alongside, same era.
P. Candelas and A. Constantin, “Completing the Web of Z 3 Z_{3} - Quotients of Complete Intersection Calabi-Yau Manifolds,” Fortsch.Phys

Then

L. B. Anderson, A. Constantin, S.-J. Lee, and A. Lukas, “Hypercharge Flux in Heterotic Compactifications,” Phys. Rev
Original
2015
Later among the works it cites.
A. Constantin, A. Lukas, and C. Mishra, “The Family Problem: Hints from Heterotic Line Bundle Models,” JHEP
Original
2016
Later among the works it cites.
E. I. Buchbinder, A. Constantin, J. Gray, and A. Lukas, “Yukawa Unification in Heterotic String Theory,” Phys. Rev
Original
2016
Later among the works it cites.
P. Candelas, A. Constantin, and C. Mishra, “Hodge Numbers for CICYs with Symmetries of Order Divisible by 4,” Fortsch. Phys
Original
2016
Later among the works it cites.
A. Constantin, J. Gray, and A. Lukas, “Hodge Numbers for All CICY Quotients,” JHEP

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2018

Formulae for Line Bundle Cohomology on Calabi-Yau Threefolds

Constantin, Andrei, Lukas, Andre

Understand

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.