Abstract
We give a systematical construction of the blowup type test configuration, named the basic blowup type test configuration, for a toric polarized variety from a torus invariant prime divisor. If the barycenter of the associated polytope is not equal to the barycenter of its facets, then we can find a torus invariant prime divisor such that the Donaldson-Futaki invariant of the associated test configuration is negative.
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Acknowledgements
The author thanks Doctors Giulio Codogni and Ruadhaí Dervan, who gave him an opportunity to publish this note, and the referee, who gave him many important comments. This work was supported by JSPS KAKENHI Grant Number 18K13388.
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Fujita, K. (2019). Notes on K-Semistability of Toric Polarized Varieties. In: Codogni, G., Dervan, R., Viviani, F. (eds) Moduli of K-stable Varieties. Springer INdAM Series, vol 31. Springer, Cham. https://doi.org/10.1007/978-3-030-13158-6_3
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DOI: https://doi.org/10.1007/978-3-030-13158-6_3
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