ELI5: Explain Like I'm 5

Semistable scheme

Alright kiddo, imagine you have a bunch of blocks that you like to stack up into a tower. Sometimes when you're building, the blocks keep falling and it's really frustrating! But sometimes, if you're careful and stack the blocks just right, they stay together and make a nice stable tower.

Now, let's talk about a semistable scheme. Imagine that instead of blocks, we have points on a graph. Sometimes, when we try to connect the points, the lines don't really make sense and the graph looks all messy. But sometimes, if we're careful, we can connect the points with lines that make sense and the graph looks nice and organized.

A semistable scheme is like that nice organized graph. It means that the lines connecting the points are as simple and straightforward as possible. And even though there might still be some places where the graph looks a little weird or messy, it's overall really structured and easy to understand.

So, just like building a tower out of blocks, it takes some skill and patience to create a semistable scheme. But when you do it right, it can make things a lot easier and clearer to see!