Betti numbers of graded modules and the multiplicity conjecture in the non-Cohen–Macaulay case
Copyright policy )Betti numbers of graded modules and the multiplicity conjecture in the non-Cohen–Macaulay case
We use the results by Eisenbud and Schreyer to prove that any Betti diagram of a graded module over a standard graded polynomial ring is a positive linear combination Betti diagrams of modules with a pure resolution. This implies the Multiplicity Conjecture of Herzog, Huneke and Srinivasan for modules that are not necessarily Cohen-Macaulay. We give a combinatorial proof of the convexity of the simplicial fan spanned by the pure diagrams.
14 pages
13A02, Mathematics - Algebraic Geometry, 13D02, FOS: Mathematics, Betti numbers, multiplicity conjecture, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), graded modules, Algebraic Geometry (math.AG)
13A02, Mathematics - Algebraic Geometry, 13D02, FOS: Mathematics, Betti numbers, multiplicity conjecture, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), graded modules, Algebraic Geometry (math.AG)
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