ON THE MONODROMY ACTION FOR f(x, y) = g(x) plus h(y)

Author(s)

Lopez-garcia, Daniel ; Valencia, Fabricio

• Document type: Journal article
• Source: Proceedings of the American Mathematical Society; v. 153, n. 5, p. 12-pg., 2025-03-05.

Abstract

We solve the problem of determining under which conditions the monodromy of a vanishing cycle generates the whole homology of a regular fiber for a polynomial f (x, y) = g(x)+h(y) where h and g are polynomials with real coefficients having real critical points and satisfying deg(g) <middle dot> deg(h) <= 2500 and gcd(deg(g), deg(h)) <= 2. As an application, under the same assumptions we solve the tangential-center problem which is known to be linked to the weak 16th Hilbert problem. (AU)

• FAPESP's process: 20/07704-7 - Morse theory on Lie groupoids and stacks
• Grantee: Fabricio Valencia Quintero
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 22/04705-8 - Poisson geometry and Lefschetz fibrations
• Grantee: Daniel Felipe López Garcia
• Support Opportunities: Scholarships in Brazil - Post-Doctoral