I tiakina i:
| Ngā kaituhi matua: | , |
|---|---|
| Hōputu: | Preprint |
| I whakaputaina: |
2026
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| Ngā marau: | |
| Urunga tuihono: | https://arxiv.org/abs/2602.20922 |
| Ngā Tūtohu: |
Tāpirihia he Tūtohu
Kāore He Tūtohu, Me noho koe te mea tuatahi ki te tūtohu i tēnei pūkete!
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Rārangi ihirangi:
- We consider the class of all homogeneous, possibly non-reduced, polynomials $f$ whose associated reduced projective divisor $D_{\text{red}} \subset \mathbb{P}^{n-1}$ has (at worst) quasi-homogeneous isolated singularities. In an arbitrary number of variables $n$ and with $d$ denoting the degree of $f$, we characterize when $-n/d$ is a root of the Bernstein--Sato polynomial of $f$ in terms of elementary data involving logarithmic derivations. When we restrict to three variables, we prove the resulting class of polynomials satisfies the Strong Monodromy Conjecture, in the motivic sense.