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Izvestiya: Mathematics, 2013, Volume 77, Issue 3, Pages 461–486
DOI: https://doi.org/10.1070/IM2013v077n03ABEH002644
(Mi im8025)
 

This article is cited in 16 scientific papers (total in 16 papers)

Ice cream and orbifold Riemann–Roch

A. Buckleya, M. Reidb, S. Zhouc

a Department of Mathematics, University of Ljubljana, Slovenia
b Mathematics Institute, University of Warwick, England
c Høgskolen i Telemark, Notodden, Norway
References:
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 $\mathrm{K3}$ 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.
Bibliography: 22 titles.
Keywords: orbifold, orbifold Riemann–Roch, Dedekind sum, Hilbert series, weighted projective varieties.
Funding agency Grant number
Korean Ministry of Education, Science and Technology R33-2008-000-10101-0
University of Warwick
Received: 02.07.2012
Revised: 22.08.2012
Bibliographic databases:
Document Type: Article
UDC: 512.7
MSC: 14Q15; 13P20
Language: English
Original paper language: English
Citation: A. Buckley, M. Reid, S. Zhou, “Ice cream and orbifold Riemann–Roch”, Izv. Math., 77:3 (2013), 461–486
Citation in format AMSBIB
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\by A.~Buckley, M.~Reid, S.~Zhou
\paper Ice cream and orbifold Riemann--Roch
\jour Izv. Math.
\yr 2013
\vol 77
\issue 3
\pages 461--486
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Linking options:
  • https://www.mathnet.ru/eng/im8025
  • https://doi.org/10.1070/IM2013v077n03ABEH002644
  • https://www.mathnet.ru/eng/im/v77/i3/p29
  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:575
    Russian version PDF:224
    English version PDF:14
    References:77
    First page:27
     
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