Blowups of Dirac structures
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916797605740544 |
|---|---|
| author | Marcut, Ioan Schüßler, Andreas Zambon, Marco |
| author_facet | Marcut, Ioan Schüßler, Andreas Zambon, Marco |
| contents | 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 $k=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14930 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blowups of Dirac structures Marcut, Ioan Schüßler, Andreas Zambon, Marco Symplectic Geometry Differential Geometry Representation Theory 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 $k=0$. |
| title | Blowups of Dirac structures |
| topic | Symplectic Geometry Differential Geometry Representation Theory |
| url | https://arxiv.org/abs/2506.14930 |