有效解决奇点
Effective resolution of singularities
Edward Bierstone, Dima Grigoriev, Pierre D. Milman, Jarosław Włodarczyk
arXiv
2025年11月10日
考虑一个投射的品种X ⊂P^n(在一个代数封闭的特征零领域),以及一个(减少的)简单的正常交叉分体E⊂P^n,其中X和E的度在最多d。 我们显示有一对(n',d'),可以用(n,d)来显式计算,这样(X,E)具有奇点(X',E')的日志分辨率,其中(X',E')可以嵌入P^n',X'和E'在P^n'中最多d'。
Consider a projective variety X ⊂ℙ^n (over an algebraically closed field of characteristic zero), together with a (reduced) simple normal crossings divisor E ⊂ℙ^n, where the degrees of both X and E are at most d. We show there is a pair (n',d') which can be explicitly computed in terms of (n,d), such that (X,E) has a log resolution of singularities (X',E'), where (X',E') can be embedded in ℙ^n' and both X' and E' have degrees at most d' in ℙ^n'.