Let $R = \mathbb{C}[x,y,u,v]$ be the coordinate ring of $\mathbb{C}^4$. Let $I$ be the ideal generated by $u$ and $v$, let $J$ be the ideal generated by $x$ and $y$. What are the flat deformations of the ideal $I^pJ^q$?

This is the ideal of the union of two non-transversely intersecting $2$-planes, with some nilpotent thickness on each plane. I would like to learn something about its smooth deformations as a subvariety of $\mathbb{C}^4$.

Let $R = \mathbf{C}[x,y,u,v]$ be the coordinate ring of $\mathbf{C}^4$. Let $I$ be the ideal generated by $u$ and $v$, let $J$ be the ideal generated by $u$ and $y$. What are the flat deformations of the ideal $I^pJ^q$?

This is the ideal of the union of two non-transversely intersecting $2$-planes, with some nilpotent thickness on each plane. I would like to learn something about its smooth deformations as a subvariety of $\mathbf{C}^4$.

Let R = C[x,y,u,v] be the coordinate ring of C^4. Let I be the ideal generated by u and v, let J be the ideal generated by x and y. What are the flat deformations of the ideal I^p J^q?

This is the ideal of the union of two non-transversely intersecting 2-planes, with some nilpotent thickness on each plane. I would like to learn something about its smooth deformations as a subvariety of C^4.

Let $R = \mathbb{C}[x,y,u,v]$ be the coordinate ring of $\mathbb{C}^4$. Let $I$ be the ideal generated by $u$ and $v$, let $J$ be the ideal generated by $x$ and $y$. What are the flat deformations of the ideal $I^pJ^q$?

This is the ideal of the union of two non-transversely intersecting $2$-planes, with some nilpotent thickness on each plane. I would like to learn something about its smooth deformations as a subvariety of $\mathbb{C}^4$.