Carregant...
Fitxers
Tipus de document
ArticleVersió
Versió acceptadaData de publicació
Tots els drets reservats
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/190625
On the arithmetic Cohen-Macaulayness of varieties parameterized by Togliatti systems
Títol de la revista
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
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.
Matèries (anglès)
Citació
Citació
COLARTE GÓMEZ, Liena, MEZZETTI, Emilia, MIRÓ-ROIG, Rosa m. (rosa maria). On the arithmetic Cohen-Macaulayness of varieties parameterized by Togliatti systems. _Annali di Matematica Pura ed Applicata_. 2021. Vol. 200, núm. 1757-1780. [consulta: 9 de abril de 2026]. ISSN: 0373-3114. [Disponible a: https://hdl.handle.net/2445/190625]