We describe conjecturally the generalized Samuel multiplicities c_0,...,c_{d-1} of a monomial ideal I subset K[x_1,...,x_d] in terms of its Newton polyhedron NP(I). More precisely, we conjecture that c_i equals the sum of the normalized (d-1)-volumes of pyramids over the projections of the (d-i-1)-dimensional compact faces of NP(I) along the infinite-directions of i-unbounded facets in which they are contained. For c_0 proofs are known (Guibert, Jeffries and Montaño) and for c_{d-1} a proof is given.
Achilles R., Manaresi M. (2022). Generalized Samuel Multiplicities of Monomial Ideals and Volumes. EXPERIMENTAL MATHEMATICS, 31(2), 611-620 [10.1080/10586458.2019.1671919].
Generalized Samuel Multiplicities of Monomial Ideals and Volumes
Achilles R.;Manaresi M.
2022
Abstract
We describe conjecturally the generalized Samuel multiplicities c_0,...,c_{d-1} of a monomial ideal I subset K[x_1,...,x_d] in terms of its Newton polyhedron NP(I). More precisely, we conjecture that c_i equals the sum of the normalized (d-1)-volumes of pyramids over the projections of the (d-i-1)-dimensional compact faces of NP(I) along the infinite-directions of i-unbounded facets in which they are contained. For c_0 proofs are known (Guibert, Jeffries and Montaño) and for c_{d-1} a proof is given.| File | Dimensione | Formato | |
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experimental.pdf
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UEXM_A_1671919_annotated.pdf
Open Access dal 08/11/2020
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Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
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