Presentations of semigroup algebras of weighted trees
Christopher Manon
DOI: 10.1007/s10801-009-0195-y
Abstract
We study presentations for subalgebras of invariants of the coordinate algebras of binary symmetric models of phylogenetic trees studied by Buczynska and Wisniewski in (J. Eur. Math. Soc. 9:609-635, 2007). These algebras arise as toric degenerations of projective coordinate rings of the moduli of weighted points on the projective line, and projective coordinate rings of the moduli of quasiparabolic semisimple rank two bundles on the projective line.
Pages: 467–489
Keywords: keywords toric ideal; polytope; phylogenetics
Full Text: PDF
References
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2. Bauer, S.: Parabolic bundles, elliptic surfaces and SU(2)-representation spaces of genus zero Fuchsian groups. Math. Ann. 290, 509-526 (1991)
3. Buczynska, W., Wisniewski, J.: On the geometry of binary symmetric models of phylogenetic trees. J. Eur. Math. Soc. 9, 609-635 (2007)
4. Castravet, A.-M., Tevelev, J.: Hilbert's 14th problem and Cox rings. Compos. Math. 142, 1479-1498 (2006)
5. Howard, B.J., Manon, C.A., Millson, J.J.: The toric geometry of triangulated polygons in Euclidean space. Can. J. Math., to appear.
6. Howard, B.J., Millson, J.J., Snowden, A., Vakil, R.: The projective invariants of ordered points on the line. arXiv:
7. Mukai, S.: Geometric realization of T -shaped root systems and counterexamples to Hilbert's fourteenth problem. In: Algebraic Transformation Groups and Algebraic Varieties. Encyclopaedia Math. Sci., vol. 132, pp. 123-129. Springer, Berlin (2004). MR2090672
8. Speyer, D., Sturmfels, B.: The tropical Grassmannian. Adv. Geom. 4, 389-411 (2004) arXiv:
9. Sturmfels, B.: Gröbner Bases and Convex Polytopes. University Lecture Series, vol. 8, American Mathematical Society, Providence (1996)
10. Sturmfels, B., Xu, Z.: Sagbi bases of Cox-Nagata rings. J. Eur. Math. Soc., to appear.
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