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Geometric interplay between function subspaces and their rings of differential operators


Authors: Rikard Bögvad and Rolf Källström
Journal: Trans. Amer. Math. Soc. 359 (2007), 2075-2108
MSC (2000): Primary 14F05, 58J99; Secondary 14L30
DOI: https://doi.org/10.1090/S0002-9947-06-03949-3
Published electronically: December 20, 2006
MathSciNet review: 2276613
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Abstract: We study, in the setting of algebraic varieties, finite-dimensional spaces of functions $ V$ that are invariant under a ring $ \mathcal{D}^V$ of differential operators, and give conditions under which $ \mathcal{D}^V$ acts irreducibly. We show how this problem, originally formulated in physics, is related to the study of principal parts bundles and Weierstrass points, including a detailed study of Taylor expansions. Under some conditions it is possible to obtain $ V$ and $ \mathcal{D}^V$ as global sections of a line bundle and its ring of differential operators. We show that several of the published examples of $ \mathcal{D}^V$ are of this type, and that there are many more--in particular, arising from toric varieties.


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Additional Information

Rikard Bögvad
Affiliation: Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden
Email: rikard@matematik.su.se

Rolf Källström
Affiliation: Department of Mathematics, University of Gävle, S-801 76 Gävle, Sweden
Email: rkm@hig.se

DOI: https://doi.org/10.1090/S0002-9947-06-03949-3
Received by editor(s): June 8, 2004
Received by editor(s) in revised form: February 5, 2005
Published electronically: December 20, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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