Geometric interplay between function subspaces and their rings of differential operators
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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.References
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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
- Received by editor(s): June 8, 2004
- Received by editor(s) in revised form: February 5, 2005
- Published electronically: December 20, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2276613