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 On the Koszul property of toric face rings


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Toric face rings is a generalization of the concepts of affine monoid rings and Stanley-Reisner rings. We consider several properties which imply Koszulness for toric face rings over a field $k$. Generalizing works of Laudal, Sletsj\o{}e and Herzog et al., graded Betti numbers of $k$ over the toric face rings are computed, and a characterization of Koszul toric face rings is provided. We investigate a conjecture suggested by R\-{o}mer about the sufficient condition for the Koszul property. The conjecture is inspired by Fr\-{o}bergs theorem on the Koszulness of quadratic squarefree monomial ideals. Finally, it is proved that initially Koszul toric face rings are affine monoid rings.



Author: Dang Hop Nguyen

Source: https://archive.org/







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