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- W2950431967 abstract "Let $Xsubsetmathbb{P}^{N}$ be an irreducible, non-degenerate variety. The generalized variety of sums of powers $VSP_H^X(h)$ of $X$ is the closure in the Hilbert scheme $Hilb_{h}(X)$ of the locus parametrizing collections of points ${x_{1},...,x_{h}}$ such that the $(h-1)$-plane $leftlangle x_{1},...,x_{h}rightrangle$ passes trough a fixed general point $pinmathbb{P}^{N}$. When $X = V_{d}^{n}$ is a Veronese variety we recover the classical variety of sums of powers $VSP(F,h)$ parametrizing additive decompositions of a homogeneous polynomial as powers of linear forms. In this paper we study the birational behavior of $VSP_H^X(h)$. In particular we will show how some birational properties, such as rationality, unirationality and rational connectedness, of $VSP_H^X(h)$ are inherited from the birational geometry of variety $X$ itself." @default.
- W2950431967 created "2019-06-27" @default.
- W2950431967 creator A5082388083 @default.
- W2950431967 date "2016-02-24" @default.
- W2950431967 modified "2023-09-23" @default.
- W2950431967 title "Generalized varieties of sums of powers" @default.
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- W2950431967 doi "https://doi.org/10.1007/s00574-016-0113-6" @default.
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