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- W4328105330 abstract "In this paper, we consider the homogeneous coordinate rings $A(Y_{n,d}) cong mathbb{K}[Omega_{n,d}]$ of monomial projections $Y_{n,d}$ of Veronese varieties parameterized by subsets $Omega_{n,d}$ of monomials of degree $d$ in $n+1$ variables where: (1) $Omega_{n,d}$ contains all monomials supported in at most $s$ variables and, (2) $Omega_{n,d}$ is a set of monomial invariants of a finite diagonal abelian group $G subset GL(n+1,mathbb{K})$ of order $d$. Our goal is to study when $mathbb{K}[Omega_{n,d}]$ is a quadratic algebra and, if so, when $mathbb{K}[Omega_{n,d}]$ is Koszul or G-quadratic. For the family (1), we prove that $mathbb{K}[Omega_{n,d}]$ is quadratic when $s ge lceil frac{n+2}{2} rceil$. For the family (2), we completely characterize when $mathbb{K}[Omega_{2,d}]$ is quadratic in terms of the group $G subset GL(3,mathbb{K})$, and we prove that $mathbb{K}[Omega_{2,d}]$ is quadratic if and only if it is Koszul. We also provide large families of examples where $mathbb{K}[Omega_{n,d}]$ is G-quadratic." @default.
- W4328105330 created "2023-03-22" @default.
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- W4328105330 date "2023-07-01" @default.
- W4328105330 modified "2023-09-23" @default.
- W4328105330 title "Monomial projections of Veronese varieties: New results and conjectures" @default.
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- W4328105330 doi "https://doi.org/10.1016/j.jalgebra.2023.03.006" @default.
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