×
Well done. You've clicked the tower. This would actually achieve something if you had logged in first. Use the key for that. The name takes you home. This is where all the applicables sit. And you can't apply any changes to my site unless you are logged in.

Our policy is best summarized as "we don't care about _you_, we care about _them_", no emails, so no forgetting your password. You have no rights. It's like you don't even exist. If you publish material, I reserve the right to remove it, or use it myself.

Don't impersonate. Don't name someone involuntarily. You can lose everything if you cross the line, and no, I won't cancel your automatic payments first, so you'll have to do it the hard way. See how serious this sounds? That's how serious you're meant to take these.

×
Register


Required. 150 characters or fewer. Letters, digits and @/./+/-/_ only.
  • Your password can’t be too similar to your other personal information.
  • Your password must contain at least 8 characters.
  • Your password can’t be a commonly used password.
  • Your password can’t be entirely numeric.
Enter the same password as before, for verification.
Login

Grow A Dic
Define A Word
Make Space
Set Task
Mark Post
Apply Votestyle
Create Votes
(From: saved spaces)
Exclude Votes
Apply Dic
Exclude Dic

A Dimca-Greuel type inequality for foliations

Click here to flash read.

arXiv:2403.18654v1 Announce Type: new
Abstract: Let $\mathcal{F}$ be a holomorphic foliation at $p\in \mathbb{C}^2$, and $B$ be a separatrix of $\mathcal{F}$. We prove the following Dimca-Greuel type inequality $\frac{\mu_p(\mathcal{F},B)}{\tau_p(\mathcal{F},B)}<4/3$, where $\mu_p(\mathcal{F},B)$ is the multiplicity of $\mathcal{F}$ along $B$ and $\tau_p(\mathcal{F},B)$ is the dimension of the quotient of $\mathbb{C}[[x,y]]$ by the ideal generated by the components of any $1$-form defining $\mathcal{F}$ and any equation of $B$. As a consequence, we provide a new proof of the $\frac{4}{3}$-Dimca-Greuel's conjecture for singularities of irreducible plane curve germs, with foliations ingredients, that differs from those given by Alberich-Carrami\~nana, Almir\'on, Blanco, Melle-Hern\'andez and Genzmer-Hernandes but it is in line with the idea developed by Wang.

Click here to read this post out
ID: 806980; Unique Viewers: 0
Unique Voters: 0
Total Votes: 0
Votes:
Latest Change: March 28, 2024, 7:32 a.m. Changes:
/u/anonymous
Dictionaries:
Words:
Spaces:
Views: 11
CC:
No creative common's license
Comments: