标题： Dirac结构的爆破 显示英文标题

标题： Blowups of Dirac structures

摘要： 给定一个实值的扭曲Dirac结构$L$和一个余维数为$>1$的光滑流形$M$上的闭嵌入子流形$N\subseteq M$，我们刻画了何时$L$可以提升为沿$M$在$N$处的实射影爆开上的光滑扭曲Dirac结构。 这精确成立当且仅当$N$要么是相对于$L$的横截子流形（没有进一步限制），要么是相对于$L$不变的子流形，并且相对于$N$的横截李代数具有相同的常数值高度$k\geq 0$。 我们还对满足这一李理论性质的李代数进行了分类。 我们重新得到了波兰丘克的一个定理，该定理指出，泊松结构可以提升到子流形的爆破上的泊松结构，当且仅当子流形是不变的并且横截李代数具有常数值高度$k=0$。 显示英文摘要

摘要： Given a real, twisted Dirac structure $L$ on a smooth manifold $M$, and a closed embedded submanifold $N\subseteq M$ of codimension $>1$, we characterise when $L$ lifts to a smooth, twisted Dirac structure on the real projective blowup of $M$ along $N$. This holds precisely when $N$ is either a submanifold transverse to $L$ (with no further restrictions) or a submanifold invariant for $L$, for which the Lie algebras transverse to $N$ have all of the same constant height $k\geq 0$. We also classify Lie algebras satisfying this Lie-theoretic property. We recover a theorem of Polishchuk, which establishes that a Poisson structure lifts to a Poisson structure on the blowup of a submanifold exactly when the submanifold is invariant and the transverse Lie algebras have constant height $k=0$.