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Algebraic Equations in State Condition

Author: Cheolgyu Lee
Journal: Proc. Amer. Math. Soc. 146 (2018), 1495-1503
MSC (2010): Primary 14L24, 03D15
Published electronically: December 4, 2017
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Abstract: In this paper, we will prove that a problem deciding whether there is an upper-triangular coordinate in which a character is not in the state of a Hilbert point is NP-hard. This problem is related to the GIT-semistability of a Hilbert point.

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Cheolgyu Lee
Affiliation: Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea – and – Department of Mathematics, POSTECH, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk, 37673, Korea.

Received by editor(s): September 25, 2016
Received by editor(s) in revised form: May 27, 2017, and June 12, 2017
Published electronically: December 4, 2017
Additional Notes: This work was supported by IBS-R003-D1. The author was partially supported by the following grants funded by the government of Korea: NRF grant 2011-0030044 (SRC-GAIA) and NRF-2013R1A1A2010649.
It is a great pleasure to thank Donghoon Hyeon, who introduced the author to the original statement and encouraged him. The author also wants to thank Junyoung Park, who pointed out that the original statement is false
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society

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