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- W4300585909 abstract "We prove a conjecture of Comon and Ottaviani that typical real Waring ranks of bivariate forms of degree $d$ take all integer values between $lfloor frac{d+2}{2}rfloor$ and $d$. That is we show that for all $d$ and all $lfloor frac{d+2}{2}rfloor leq m leq d$ there exists a bivariate form $f$ such that $f$ can be written as a linear combination of $m$ $d$-th powers of real linear forms and no fewer, and additionally all forms in an open neighborhood of $f$ also possess this property. Equivalently we show that for all $d$ and any $lfloor frac{d+2}{2}rfloor leq m leq d$ there exists a symmetric real bivariate tensor $t$ of order $d$ such that $t$ can be written as a linear combination of $m$ symmetric real tensors of rank 1 and no fewer, and additionally all tensors in an open neighborhood of $t$ also possess this property." @default.
- W4300585909 created "2022-10-03" @default.
- W4300585909 creator A5045938141 @default.
- W4300585909 date "2012-05-15" @default.
- W4300585909 modified "2023-09-30" @default.
- W4300585909 title "Typical Real Ranks of Binary Forms" @default.
- W4300585909 doi "https://doi.org/10.48550/arxiv.1205.3257" @default.
- W4300585909 hasPublicationYear "2012" @default.
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