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Orbifold Riemann-Roch and Hilbert series
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Zhou, Shengtian (2011) Orbifold Riemann-Roch and Hilbert series. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2669676~S1
Abstract
A general Riemann-Roch formula for smooth Deligne-Mumford stacks was
obtained by Toen [Toë99]. Using this formula, we obtain an explicit Riemann-Roch formula for quasismooth substacks of weighted projective space, following
the ideas in [Nir]. The Riemann-Roch formula enables us to study polarized orbifolds in terms of the associated Hilbert series. Given a polarized projectively
Gorenstein quasismooth pair (X, Od∈Z O(d)), we want to parse the Hilbert series P(t) = ∑d>=0 h0(X,OX (d))td according to the orbifold loci. For X with only isolated orbifold points, we give a parsing such that each orbifold point corresponds to
a closed term, which only depends on the orbifold type of the point and has Goresntein symmetry property and integral coefficients. Similarly, for the case when X
has dimension <= 1 orbifold loci, we can also parse the Hilbert series into closed
terms corresponding to orbifold curves and dissident points as well as isolated orbifold points. Our parsing of Hilbert series reflects the global symmetry property of
the Gorenstein ring Od>=0 H0(X,OX (d))td in terms of its local data.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Riemann-Roch theorems, Algebraic stacks, Orbifolds | ||||
Official Date: | March 2011 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Reid, Miles (Miles A.) | ||||
Sponsors: | University of Warwick ; Korea (R33-2008-000-10101-0) | ||||
Extent: | v, 91 leaves | ||||
Language: | eng |
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