Extremal Bundles on Calabi-Yau Threefolds

Gao, P., He, Y. & Yau, S-T. (2014). Extremal Bundles on Calabi-Yau Threefolds. Communications in Mathematical Physics, 336(3), pp. 1167-1200. doi: 10.1007/s00220-014-2271-y

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We study constructions of stable holomorphic vector bundles on Calabi–Yau threefolds, especially those with exact anomaly cancellation which we call extremal. By going through the known databases we find that such examples are rare in general and can be ruled out for the spectral cover construction for all elliptic threefolds. We then introduce a general Hartshorne–Serre construction and use it to find extremal bundles of general ranks and study their stability, as well as computing their Chern numbers. Based on both existing and our new constructions, we revisit the DRY conjecture for the existence of stable sheaves on Calabi–threefolds, and provide theoretical and numerical evidence for its correctness. Our construction can be easily generalized to bundles with no extremal conditions imposed.

Item Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-014-2271-y
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/12856

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