The graph of monomial ideals
Copyright policy )The graph of monomial ideals
There is a natural infinite graph whose vertices are the monomial ideals in a polynomial ring. The definition involves Gr��bner bases or the action of an algebraic torus. We present algorithms for computing the (affine schemes representing) edges in this graph. We study the induced subgraphs on multigraded Hilbert schemes and on square-free monomial ideals. In the latter case, the edges correspond to generalized bistellar flips.
15 pages, Latex
- Freie Universität Berlin Germany
- University of California, Berkeley United States
graph of monomial ideals, Algebra and Number Theory, Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Grassmannians, Schubert varieties, flag manifolds, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Schubert scheme, Stanley-Reisner ideals, Parametrization (Chow and Hilbert schemes), multigraded Hilbert scheme, FOS: Mathematics, Gröbner bases, Gröbner degenerations, 13P10 (Primary) 14L30, 52B70 (Secondary)
graph of monomial ideals, Algebra and Number Theory, Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Grassmannians, Schubert varieties, flag manifolds, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Schubert scheme, Stanley-Reisner ideals, Parametrization (Chow and Hilbert schemes), multigraded Hilbert scheme, FOS: Mathematics, Gröbner bases, Gröbner degenerations, 13P10 (Primary) 14L30, 52B70 (Secondary)
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