Resolution of singularities
Resolution of singularities is like smoothing out a bumpy road so that cars can drive on it smoothly without any bumps. In the same way, in math, we want to make sure that our shapes and equations don't have any bumpy parts called singularities.
Imagine drawing a shape like a cone or a cylinder. These shapes are smooth and don't have any bumps or holes. But if you try to draw a more complicated shape like a twisted rope, you might end up with bumps or holes in some parts of the shape. These bumps are called singularities.
So, when we do the resolution of singularities, we try to "fix" these bumps or holes and make the shape smooth again. To do this, we might need to cut out some parts of the shape, move some parts around, or add some new pieces to the shape.
The goal is to end up with a new shape that is smooth and doesn't have any bumps or holes. This new shape is called a "resolution" of the original shape.
Just like how cars can drive smoothly on a newly paved road, mathematicians can work with the smooth, resolved shape without any problems.
Imagine drawing a shape like a cone or a cylinder. These shapes are smooth and don't have any bumps or holes. But if you try to draw a more complicated shape like a twisted rope, you might end up with bumps or holes in some parts of the shape. These bumps are called singularities.
So, when we do the resolution of singularities, we try to "fix" these bumps or holes and make the shape smooth again. To do this, we might need to cut out some parts of the shape, move some parts around, or add some new pieces to the shape.
The goal is to end up with a new shape that is smooth and doesn't have any bumps or holes. This new shape is called a "resolution" of the original shape.
Just like how cars can drive smoothly on a newly paved road, mathematicians can work with the smooth, resolved shape without any problems.