Convex bodies and multiplicities of ideals
By Kiumars Kaveh, Askold Khovanskii. 2013
52 citations recorded by the source corpus.
We associate convex regions in ℝn to m-primary graded sequences of subspaces, in particular m-primary graded sequences of ideals, in a large class of local algebras (including analytically irreducible local domains). These convex regions encode information about Samuel multiplicities. This is in the spirit of the theory of Gröbner bases and Newton polyhedra on the one hand, and the theory of Newton-Okounkov bodies for linear systems on the other hand. We use this to give a new proof as well as a generalization of a Brunn-Minkowski inequality for multiplicities due to Teissier and Rees-Sharp.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/4743ccb075c4ce8023003e5371bd553c7ede482b
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- K-semistability is equivariant volume minimization (2015, methodology): “ivation of this formula uses the tool of ltrations (see [BC11]) and has a very concrete convex geometric meaning which allows us to use the theory of Okounkov bodies ([Oko96,LM09]) and coconvex sets ([KK14]) to understand it. Given this formula, then as in [Li15a] we can take its derivative and use ”