Computing the Roots of Twisting Sheaves over the Projective Line arising from Monodromy Representations
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909447907966976 |
|---|---|
| author | Yépez, Diego |
| author_facet | Yépez, Diego |
| contents | Given a monodromy representation $ρ$ of the projective line minus $m$ points, one can extend the resulting vector bundle with connection map canonically to a vector bundle with logarithmic connection map over all of the projective line. Now, since vector bundles split as twisting sheaves over the projective line, the focus of this work regards knowing the exact decomposition; i.e. computing the roots. Particularly, we compute the roots for all finite-dimensional $ρ$ when $m = 2$ and for all $ρ$ of dimension less than $3$ when $m = 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01006 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing the Roots of Twisting Sheaves over the Projective Line arising from Monodromy Representations Yépez, Diego Algebraic Geometry Complex Variables 14F06, 32L10 Given a monodromy representation $ρ$ of the projective line minus $m$ points, one can extend the resulting vector bundle with connection map canonically to a vector bundle with logarithmic connection map over all of the projective line. Now, since vector bundles split as twisting sheaves over the projective line, the focus of this work regards knowing the exact decomposition; i.e. computing the roots. Particularly, we compute the roots for all finite-dimensional $ρ$ when $m = 2$ and for all $ρ$ of dimension less than $3$ when $m = 3$. |
| title | Computing the Roots of Twisting Sheaves over the Projective Line arising from Monodromy Representations |
| topic | Algebraic Geometry Complex Variables 14F06, 32L10 |
| url | https://arxiv.org/abs/2501.01006 |