2026-04-17T21:38:33Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/1906252025-12-05T09:59:09Zcom_2072_1057col_2072_478917col_2072_478920

00925njm 22002777a 4500 dc Colarte Gómez, Liena author Mezzetti, Emilia author Miró-Roig, Rosa M. (Rosa Maria) author 2022-11-09T09:08:46Z 2022-11-09T09:08:46Z 2021-01-06 2022-11-09T09:08:46Z 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. 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