- Tags: - #todo/untagged - Refs: - #todo/add-references - Links: - Types of divisors: - big - nef divisor - Weil divisor - Cartier divisor - Ample divisor - irreducible divisor - O(D) for D a divisor - linearly equivalent divisors - Weil reciprocity - Neron Severi

A blow-up is a rational morphism transformation that replaces a closed subscheme with an effective Cartier divisor. Precisely, given a Noetherian scheme \(X\) and a closed subscheme \(Z \subset X\), the blow-up of \(X\) along \(Z\) is a proper morphism \(\pi: \widetilde{X} \rightarrow X\) such that

Tags: #AG Refs: Cartier divisor dualizing sheaf canonical divisor