The zero set of semi-invariants for extended Dynkin quivers
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- by Ch. Riedtmann and G. Zwara PDF
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Abstract:
We show that the set of common zeros $\mathcal {Z}_{Q,\mathbf {d}}$ of all semi-invariants vanishing at $0$ on the variety $\operatorname {rep}(Q,\mathbf {d})$ of all representations with dimension vector $\mathbf {d}$ of an extended Dynkin quiver $Q$ under the group $\operatorname {GL}(\mathbf {d})$ is a complete intersection if $\mathbf {d}$ is “big enough”. In case $\operatorname {rep}(Q,\mathbf {d})$ does not contain an open $\operatorname {GL}(\mathbf {d})$-orbit, which is the case not considered so far, the number of irreducible components of $\mathcal {Z}_{Q,\mathbf {d}}$ grows with $\mathbf {d}$, except if $Q$ is an oriented cycle.References
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Additional Information
- Ch. Riedtmann
- Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
- Email: christine.riedtmann@math-stat.unibe.ch
- G. Zwara
- Affiliation: Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
- Email: gzwara@mat.uni.torun.pl
- Received by editor(s): October 12, 2006
- Published electronically: July 21, 2008
- Additional Notes: The second author gratefully acknowledges support from the Polish Scientific Grant KBN No. 1 P03A 018 27 and the Swiss Science Foundation.
- © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 360 (2008), 6251-6267
- MSC (2000): Primary 14L24; Secondary 16G20
- DOI: https://doi.org/10.1090/S0002-9947-08-04613-8
- MathSciNet review: 2434286