A-graded methods for monomial ideals
Christine Berkesch, Laura Felicia Matusevich
TL;DR
This paper introduces multigraded techniques based on zz^d-gradings and the Koszul functor to analyze d-dimensional monomial ideals, connecting algebraic and geometric perspectives and enabling explicit computation of multiplicities.
Contribution
It develops a novel multigraded framework using zz^d-gradings and the Koszul functor to study monomial ideals, linking hypergeometric systems with algebraic geometry.
Findings
Explicit computation of multiplicities of exponents.
Interpretation of quasidegrees via geometry of distractions.
Application of multigraded techniques from hypergeometric systems.
Abstract
We use \ZZ^d-gradings to study d-dimensional monomial ideals. The Koszul functor is employed to interpret the quasidegrees of local cohomology in terms of the geometry of distractions and to explicitly compute the multiplicities of exponents. These multigraded techniques originate from the study of hypergeometric systems of differential equations.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Polynomial and algebraic computation