2026-04-13T02:30:34Zhttps://recercat.cat/oai/requestoai:recercat.cat:2445/1906252025-12-05T09:59:09Zcom_2072_1057col_2072_478917col_2072_478920
RECERCAT
author
Colarte Gómez, Liena
author
Mezzetti, Emilia
author
Miró-Roig, Rosa M. (Rosa Maria)
2022-11-09T09:08:46Z2022-11-09T09:08:46Z2021-01-062022-11-09T09:08:46Z
Given any diagonal cyclic subgroup $\Lambda \subset G L(n+1, k)$ of order $d$, let $I_d \subset k\left[x_0, \ldots, x_n\right]$ be the ideal generated by all monomials $\left\{m_1, \ldots, m_r\right\}$ of degree $d$ which are invariants of $\Lambda . I_d$ is a monomial Togliatti system, provided $r \leq\left(\begin{array}{c}d+n-1 \\ n-1\end{array}\right)$, and in this case the projective toric variety $X_d$ parameterized by $\left(m_1, \ldots, m_r\right)$ is called a $G T$-variety with group $\Lambda$. We prove that all these $G T$-varieties are arithmetically Cohen-Macaulay and we give a combinatorial expression of their Hilbert functions. In the case $n=2$, we compute explicitly the Hilbert function, polynomial and series of $X_d$. We determine a minimal free resolution of its homogeneous ideal and we show that it is a binomial prime ideal generated by quadrics and cubics. We also provide the exact number of both types of generators. Finally, we pose the problem of determining whether a surface parameterized by a Togliatti system is aCM. We construct examples that are aCM and examples that are not.
(c) Springer Verlag, 2021 info:eu-repo/semantics/openAccess
Varietats algebraiques
Anells commutatius
Mòduls de Cohen-Macaulay
Grups algebraics diferencials
Algebraic varieties
Commutative rings
Cohen-Macaulay modules
Differential algebraic groups
On the arithmetic Cohen-Macaulayness of varieties parameterized by Togliatti systems
info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion