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We present a library autgradalg.lib for the free computer algebra system Singular to compute automorphisms of integral, finitely generated $mathbb{C}$-algebras that are graded pointedly by a finitely generated abelian group. It implements the algorithms developed in Computing automorphisms of Mori dream spaces. We apply the algorithms to Mori dream spaces and investigate the automorphism groups of a series of Fano varieties.
We study the notion of $Gamma$-graded commutative algebra for an arbitrary abelian group $Gamma$. The main examples are the Clifford algebras already treated by Albuquerque and Majid. We prove that the Clifford algebras are the only simple finite-dim
Let $R$ be the power series ring or the polynomial ring over a field $k$ and let $I $ be an ideal of $R.$ Macaulay proved that the Artinian Gorenstein $k$-algebras $R/I$ are in one-to-one correspondence with the cyclic $R$-submodules of the divided p
We introduce the Macaulay2 package $mathtt{LinearTruncations}$ for finding and studying the truncations of a multigraded module over a standard multigraded ring that have linear resolutions.
We prove the existence of HK density function for a pair $(R, I)$, where $R$ is a ${mathbb N}$-graded domain of finite type over a perfect field and $Isubset R$ is a graded ideal of finite colength. This generalizes our earlier result where one prove
We study the symmetric subquotient decomposition of the associated graded algebras $A^*$ of a non-homogeneous commutative Artinian Gorenstein (AG) algebra $A$. This decomposition arises from the stratification of $A^*$ by a sequence of ideals $A^*=C_