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Ice cream and orbifold Riemann-Roch
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Buckley, Anita, Reid, Miles and Zhou, Shengtian (2013) Ice cream and orbifold Riemann-Roch. Izvestiya: Mathematics, Volume 77 (Number 3). pp. 461-486. doi:10.1070/IM2013v077n03ABEH002644 ISSN 1064-5632.
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Official URL: http://dx.doi.org/10.1070/IM2013v077n03ABEH002644
Abstract
We give an orbifold Riemann-Roch formula in closed form for the Hilbert series of a quasismooth polarized n-fold (X,D), under the assumption that X is projectively Gorenstein with only isolated orbifold points. Our formula is a sum of parts each of which is integral and Gorenstein symmetric of the same canonical weight; the orbifold parts are called ice cream functions. This form of the Hilbert series is particularly useful for computer algebra, and we illustrate it on examples of K3 surfaces and Calabi-Yau 3-folds. These results apply also with higher dimensional orbifold strata (see [1] and [2]), although the precise statements are considerably trickier. We expect to return to this in future publications.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Izvestiya: Mathematics | ||||
Publisher: | Turpion Ltd. | ||||
ISSN: | 1064-5632 | ||||
Official Date: | 2013 | ||||
Dates: |
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Volume: | Volume 77 | ||||
Number: | Number 3 | ||||
Page Range: | pp. 461-486 | ||||
DOI: | 10.1070/IM2013v077n03ABEH002644 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
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