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arXiv · 2512.17871

Cellular free resolutions for normalizations of toric ideals

Christine Berkesch·Lauren Cranton Heller·Gregory G. Smith·Jay Yang
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Abstract

For any toric ideal $I$ in a polynomial ring $S$, we provide a combinatorial description of a free resolution of the integral closure of the $S$-module $S/I$. These new complexes arise from an extension of Bayer--Sturmfels' theory of cellular free resolutions. As applications, we unify several constructions for a resolution of the diagonal embedding of a toric variety, and compare the locally free resolutions for toric subvarieties introduced by Hanlon--Hicks--Lazarev and Brown--Erman.

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Christine Berkesch, Lauren Cranton Heller, Gregory G. Smith, Jay Yang. 2025-12-19. Cellular free resolutions for normalizations of toric ideals. https://arxiv.org/abs/2512.17871

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