This thesis focuses on weighted blow-ups. Weighted blow-ups are an important class of birational transformations, which has, for stacks, a similar role to the one of ordinary blow-up for schemes. They appear naturally in resolution of singularities and in the study of moduli spaces. Firstly we will first focus on the blow-up map, and give a non-obstructedness result for blow-downs. Later, we will focus on the intersection theory of the weighted blow-up stack, and give a criterion for its Chow ring with integral coefficients. This is a consequence of a generalization of the sequence Fulton calls the key sequence, which we prove in order to get the final result. Lastly we will look at the key sequence with rational coefficients to prove a weighted version of Fulton’s Blow-up formula, which studies the difference between the proper transform and the pullback of a closed substack of the center.
