Advances on a conjecture about free divisors
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912754657394688 |
|---|---|
| author | Rodríguez, Abraham del Valle |
| author_facet | Rodríguez, Abraham del Valle |
| contents | In 2002, it was conjectured that a free divisor satisfying the so-called Logarithmic Comparison Theorem (LCT) must be strongly Euler-homogeneous. Today, it is known to be true only in ambient dimension less or equal than three or assuming Koszul-freeness. Thanks to our advances in the comprehension of strong Euler-homogeneity, we are able to prove the conjecture in the following new cases: assuming strong Euler-homogeneity on a punctured neighbourhood of a point; assuming the divisor is weakly Koszul-free; for ambient dimension $n=4$; for linear free divisors in ambient dimension $n=5$. We also refute a conjecture that states that all linear free divisors satisfy LCT and are strongly Euler-homogeneous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21834 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Advances on a conjecture about free divisors Rodríguez, Abraham del Valle Algebraic Geometry Complex Variables 32S25 (Primary), 32S05, 14F40 (Secondary) In 2002, it was conjectured that a free divisor satisfying the so-called Logarithmic Comparison Theorem (LCT) must be strongly Euler-homogeneous. Today, it is known to be true only in ambient dimension less or equal than three or assuming Koszul-freeness. Thanks to our advances in the comprehension of strong Euler-homogeneity, we are able to prove the conjecture in the following new cases: assuming strong Euler-homogeneity on a punctured neighbourhood of a point; assuming the divisor is weakly Koszul-free; for ambient dimension $n=4$; for linear free divisors in ambient dimension $n=5$. We also refute a conjecture that states that all linear free divisors satisfy LCT and are strongly Euler-homogeneous. |
| title | Advances on a conjecture about free divisors |
| topic | Algebraic Geometry Complex Variables 32S25 (Primary), 32S05, 14F40 (Secondary) |
| url | https://arxiv.org/abs/2504.21834 |