ABSTRACT
We generalize the concept of r-point clusters of a scheme S to r-relative clusters of a B-scheme 𝒮, and define schemes Clr that naturally parametrize them. In the particular case that B = SpecK, the schemes Clr agree with Kleiman’s iterated blowups parametrizing r-point clusters. We show that there is an iterative construction of Clr + 1 from Clr, related but not equal in general to the blow up of along the diagonal.
Acknowledgments
I thank my thesis advisor, Joaquim Roć, for his great support and I thank the referee for the patience and all the feedback.