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math.CO 1

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2026 1

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Vector fields of graphic arrangements and face rings of simplicial posets

math.CO · 2026-08-07 · conditional · novelty 8.0

For a connected graph G, the modified logarithmic vector field D_R(A_G) is isomorphic as an R-module to the face ring K[P_G] of an explicitly constructed simplicial poset, yielding new formulas for Hilbert series, local cohomology, projective dimension, and regularity.

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  • Vector fields of graphic arrangements and face rings of simplicial posets math.CO · 2026-08-07 · conditional · none · ref 7

    For a connected graph G, the modified logarithmic vector field D_R(A_G) is isomorphic as an R-module to the face ring K[P_G] of an explicitly constructed simplicial poset, yielding new formulas for Hilbert series, local cohomology, projective dimension, and regularity.