Gluing schemes
Okay, so let's say you have two pieces of paper and you want to stick them together. You can use glue to make sure they stay together.
Now, imagine you have two different shapes on those papers. Maybe one has a circle and the other has a square. You can still use glue to stick them together, but you have to be careful that you glue the right part of the circle to the right part of the square so that they fit together nicely.
When we talk about gluing "schemes", we're talking about doing something similar but with more complicated shapes. Schemes are like big, complicated shapes made up of lots of smaller shapes.
When we "glue" two schemes together, we're actually "gluing" together two smaller pieces of each scheme that match up nicely. This makes a new, bigger scheme that is made up of the two smaller ones.
But sometimes, the two pieces we want to "glue" don't match up as nicely as we want them to. In those cases, we might have to change one or both of the schemes a little bit to make them fit nicely when we "glue" them together. This can be tricky, but it's an important part of working with schemes.
Now, imagine you have two different shapes on those papers. Maybe one has a circle and the other has a square. You can still use glue to stick them together, but you have to be careful that you glue the right part of the circle to the right part of the square so that they fit together nicely.
When we talk about gluing "schemes", we're talking about doing something similar but with more complicated shapes. Schemes are like big, complicated shapes made up of lots of smaller shapes.
When we "glue" two schemes together, we're actually "gluing" together two smaller pieces of each scheme that match up nicely. This makes a new, bigger scheme that is made up of the two smaller ones.
But sometimes, the two pieces we want to "glue" don't match up as nicely as we want them to. In those cases, we might have to change one or both of the schemes a little bit to make them fit nicely when we "glue" them together. This can be tricky, but it's an important part of working with schemes.