Timeline for How does multiplication affect degrees?

9 events

when toggle format	what		by	license	comment
Feb 11, 2019 at 17:32	history	edited	YCor		edited tags
Oct 20, 2018 at 10:50	answer	added	H A Helfgott		timeline score: 1
Oct 20, 2018 at 10:28	answer	added	Jason Starr		timeline score: 5
Oct 20, 2018 at 10:21	comment	added	Jason Starr		I forgot the equations for $V$ and $W$: $x_{1,1}-x_{1,2}$, resp. $x_{2,2}-x_{1,2}$. I will post it as an answer below.
Oct 20, 2018 at 7:47	history	edited	H A Helfgott	CC BY-SA 4.0	deleted 1 character in body
Oct 20, 2018 at 7:39	history	edited	H A Helfgott	CC BY-SA 4.0	deleted 1 character in body
Oct 20, 2018 at 7:26	comment	added	H A Helfgott		Sorry, but for some reason I am not getting the equation $2 x_{1,1} x_{2,2} - x_{1,2}$. (Moreover, the dimension of V and W is 2.) Are you sure this is right? I get that the degree of the product is 1.
Oct 20, 2018 at 0:53	comment	added	Jason Starr		That is not true. Let $n$ be $2$. Let $G$ be $\textbf{GL}_2$ with its open immersion in $\mathbb{A}^{2^2}$. Denote the $(i,j)$ entry of a matrix by $x_{i,j}$. Let $V$ be the $1$-dimensional, affine linear subspace $\text{Zero}(x_{2,1},x_{2,2}-1)$. Let $W$ be the $1$-dimensional, affine linear subspace $\text{Zero}(x_{1,1}-1,x_{2,1})$. Then $\overline{V\cdot W}$ is the $2$-dimensional subvariety $\text{Zero}(x_{2,1},2x_{1,1}x_{2,2}-x_{1,2})$. This has degree $2$.
Oct 20, 2018 at 0:20	history	asked	H A Helfgott	CC BY-SA 4.0