p-Anisotropy on the Moment Curve for Homology Manifolds and Cycles

Karim Alexander Adiprasito; Kaiying Hou; Daishi Kiyohara; Daniel Koizumi; Monroe Stephenson

doi:10.1007/s00493-025-00192-w

p-Anisotropy on the Moment Curve for Homology Manifolds and Cycles

Karim Alexander Adiprasito^*
, Kaiying Hou
, Daishi Kiyohara
, Daniel Koizumi
, Monroe Stephenson

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the Gorensteinification of the face ring of a cycle is totally p-anisotropic in characteristic p. In other words, given an appropriate Artinian reduction, it contains no nonzero p-isotropic elements. Moreover, we prove that the linear system of parameters can be chosen corresponding to a geometric realization with points on the moment curve. In particular, this implies that the parameters do not have to be chosen very generically.

Original language	English
Article number	65
Journal	Combinatorica
Volume	45
Issue number	6
DOIs	https://doi.org/10.1007/s00493-025-00192-w
State	Published - Dec 2025
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2025.

Keywords

Anisotropy
Face rings
Hard Lefschetz theorem
Moment curve
Simplicial cycles

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10.1007/s00493-025-00192-w

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abstract = "We prove that the Gorensteinification of the face ring of a cycle is totally p-anisotropic in characteristic p. In other words, given an appropriate Artinian reduction, it contains no nonzero p-isotropic elements. Moreover, we prove that the linear system of parameters can be chosen corresponding to a geometric realization with points on the moment curve. In particular, this implies that the parameters do not have to be chosen very generically.",

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AU - Adiprasito, Karim Alexander

AU - Hou, Kaiying

AU - Kiyohara, Daishi

AU - Koizumi, Daniel

AU - Stephenson, Monroe

N1 - Publisher Copyright: © The Author(s), under exclusive licence to János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2025.

PY - 2025/12

Y1 - 2025/12

N2 - We prove that the Gorensteinification of the face ring of a cycle is totally p-anisotropic in characteristic p. In other words, given an appropriate Artinian reduction, it contains no nonzero p-isotropic elements. Moreover, we prove that the linear system of parameters can be chosen corresponding to a geometric realization with points on the moment curve. In particular, this implies that the parameters do not have to be chosen very generically.

AB - We prove that the Gorensteinification of the face ring of a cycle is totally p-anisotropic in characteristic p. In other words, given an appropriate Artinian reduction, it contains no nonzero p-isotropic elements. Moreover, we prove that the linear system of parameters can be chosen corresponding to a geometric realization with points on the moment curve. In particular, this implies that the parameters do not have to be chosen very generically.

KW - Anisotropy

KW - Face rings

KW - Hard Lefschetz theorem

KW - Moment curve

KW - Simplicial cycles

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ER -

p-Anisotropy on the Moment Curve for Homology Manifolds and Cycles

Abstract

Bibliographical note

Keywords

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