Toric degenerations and vector bundles

Gubeladze, Joseph

doi:10.1090/S0002-9939-99-05009-1

Toric degenerations and vector bundles
HTML articles powered by AMS MathViewer

by Joseph Gubeladze PDF

Proc. Amer. Math. Soc. 127 (1999), 3493-3494 Request permission

Abstract:

There are many affine subalgebras of polynomial rings with highly non-trivial projective modules, whose initial algebras (toric degenerations) are still finitely generated and have all projective modules free.

References

Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491
Aldo Conca, Jürgen Herzog, and Giuseppe Valla, Sagbi bases with applications to blow-up algebras, J. Reine Angew. Math. 474 (1996), 113–138. MR 1390693, DOI 10.1515/crll.1996.474.113
I. Dzh. Gubeladze, The Anderson conjecture and a maximal class of monoids over which projective modules are free, Mat. Sb. (N.S.) 135(177) (1988), no. 2, 169–185, 271 (Russian); English transl., Math. USSR-Sb. 63 (1989), no. 1, 165–180. MR 937805, DOI 10.1070/SM1989v063n01ABEH003266
Joseph Gubeladze, Nontriviality of $SK_1(R[M])$, J. Pure Appl. Algebra 104 (1995), no. 2, 169–190. MR 1360174, DOI 10.1016/0022-4049(94)00130-1
Lorenzo Robbiano and Moss Sweedler, Subalgebra bases, Commutative algebra (Salvador, 1988) Lecture Notes in Math., vol. 1430, Springer, Berlin, 1990, pp. 61–87. MR 1068324, DOI 10.1007/BFb0085537
V. Srinivas, $K_1$ of the cone over a curve, J. Reine Angew. Math. 381 (1987), 37–50. MR 918839, DOI 10.1515/crll.1987.381.37