On the Multiplication Map of a Multigraded Algebra
نویسنده
چکیده
Given a multigraded algebra A, it is a natural question whether or not for two homogeneous components Au and Av, the product AnuAnv is the whole component Anu+nv for n big enough. We give combinatorial and geometric answers to this question. 1. Statement and discussion of the results In this note, we consider the multiplication map of a multigraded algebra and ask for its surjectivity properties on the homogeneous parts. More precisely, let A be an (associative, commutative), integral, finitely generated algebra (with unit) over an algebraically closed field K, and suppose that A is graded by a lattice M ∼= Z, i.e., we have A = ⊕
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