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YCor
YCor
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when When is a degree-n$n$ homogeneous polynomial in $\mathbb{C}[x_1, x_2, \ldots , x_m ]$ the product of n$n$ one-forms?

When is a degree-$n$ homogeneous polynomial in $\mathbb{C}[x_1, x_2, \ldots , x_m ]$ the product of $n$ one-forms?

Is there any simple algorithm or criterion to check it?

I have choosenchosen the complex field to avoid any field insufficiency.

when is a degree-n homogeneous polynomial in $\mathbb{C}[x_1, x_2, \ldots , x_m ]$ the product of n one-forms?

Is there any simple algorithm or criterion to check it?

I have choosen the complex field to avoid any field insufficiency.

When is a degree-$n$ homogeneous polynomial in $\mathbb{C}[x_1, x_2, \ldots , x_m ]$ the product of $n$ one-forms?

When is a degree-$n$ homogeneous polynomial in $\mathbb{C}[x_1, x_2, \ldots , x_m ]$ the product of $n$ one-forms?

Is there any simple algorithm or criterion to check it?

I have chosen the complex field to avoid any field insufficiency.

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poisson
poisson
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when is a degree-n homogeneous polynomial in $\mathbb{C}[x_1, x_2, \ldots , x_m ]$ the product of n one-forms?

Is there any simple algorithm or criterion to check it?

I have choosen the complex field to avoid any field insufficiency.