논문KCI 등재
STABILITY COMPUTATION VIA GR¨OBNER BASIS
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초록
In this article, we discuss a Gr¨obner basis algorithm related to the stability of algebraic varieties in the sense of Geometric Invariant Theory. We implement the algorithm with Macaulay 2 and use it to prove the stability of certain curves that play an important role in the log minimal model program for the moduli space of curves.
Abstract
In this article, we discuss a Gr¨obner basis algorithm related to the stability of algebraic varieties in the sense of Geometric Invariant Theory. We implement the algorithm with Macaulay 2 and use it to prove the stability of certain curves that play an important role in the log minimal model program for the moduli space of curves.
참고문헌 (12)
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- D. Eisenbud, "Commutative Algebra, Graduate Texts in Mathematics, 150" (1995), Springer-Verlag
- "Macaulay 2, a software system for research in algebraic geometry"[URL]
- B. Hassett, "Log canonical models for the moduli space of curves: The first flip, arXiv:math.AG", 0806.3444v1, 2008
- D. Hyeon, "Stability of bicanonical curves of genus three", Journal of Pure and Applied Algebra (2009)
- D. Hyeon, "Log minimal model program for the moduli space of stable curves of genus three, arXiv:math.AG", 0703093, 2007
- D. Hyeon, "Stability of tri-canonical curves of genus two", Math. Ann., 337(2), pp.479~488 (2007)
- M. Kapranov, "Chow polytopes and general resultants", Duke Math. J., 67(1), pp.189~218 (1992)
- F. Knudsen, "The projectivity of the moduli space of stable curves. I, Preliminaries on “det” and “Div”", Math. Scand., 39(1), pp.19~55 (1976)
- I. Morrison, "Projective stability of ruled surfaces", Invent. Math., 56(3), pp.269~304 (1980)
- D. Schubert, "A new compactification of the moduli space of curves", Compositio Math., 78(3), pp.297~313 (1991)
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