Excess logarithmic residues for foliations by curves and applications
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911628160663552 |
|---|---|
| author | Cavalcante, Alana Corrêa, Maurício Lourenço, Fernando Shahsavaripour, Elaheh |
| author_facet | Cavalcante, Alana Corrêa, Maurício Lourenço, Fernando Shahsavaripour, Elaheh |
| contents | We introduce excess logarithmic residues for one-dimensional holomorphic foliations tangent to a divisor. They arise from the comparison between the logarithmic normal sheaf and the ordinary normal sheaf of the foliation, and measure the local variation between the logarithmic and classical Baum--Bott contributions. We prove a global residue formula expressing the corresponding Chern numbers as sums of local residues. We then derive a Poincaré-type bound for invariant hypersurfaces from the non-negativity of the relevant logarithmic residues. Finally, for a normal \(\mathbb Q\)-Gorenstein surface $Y$, we show that the componentwise logarithmic residues of a lifted foliation along the exceptional divisor of a functorial resolution recover the log discrepancies of the singularities of $Y$, giving a dynamical and foliated test for log canonicity of these singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25395 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Excess logarithmic residues for foliations by curves and applications Cavalcante, Alana Corrêa, Maurício Lourenço, Fernando Shahsavaripour, Elaheh Algebraic Geometry Complex Variables Differential Geometry We introduce excess logarithmic residues for one-dimensional holomorphic foliations tangent to a divisor. They arise from the comparison between the logarithmic normal sheaf and the ordinary normal sheaf of the foliation, and measure the local variation between the logarithmic and classical Baum--Bott contributions. We prove a global residue formula expressing the corresponding Chern numbers as sums of local residues. We then derive a Poincaré-type bound for invariant hypersurfaces from the non-negativity of the relevant logarithmic residues. Finally, for a normal \(\mathbb Q\)-Gorenstein surface $Y$, we show that the componentwise logarithmic residues of a lifted foliation along the exceptional divisor of a functorial resolution recover the log discrepancies of the singularities of $Y$, giving a dynamical and foliated test for log canonicity of these singularities. |
| title | Excess logarithmic residues for foliations by curves and applications |
| topic | Algebraic Geometry Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2604.25395 |