On the monodromy conjecture, holomorphy conjecture, and embedded Nash problem for Pfaffian ideals

2025/11/03 by Chen, Yifan, Shi, Quan, Xu, Yongxin +1
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.01262

Abstract

We resolve the monodromy conjecture, holomorphy conjecture, and embedded Nash problem for Pfaffian ideals.

Citations

• Polar loci of multivariable archimedean zeta functions
• On the Tensor Property of Bernstein-Sato Polynomial
• On contact loci of hyperplane arrangements
• Zero loci of Bernstein-Sato ideals
• The holomorphy conjecture for nondegenerate surface singularities
• On the monodromy conjecture for non-degenerate hypersurfaces
• The monodromy conjecture for zeta functions associated to ideals in dimension two
• The holomorphy conjecture for ideals in dimension two
• Bernstein-Sato polynomials of arbitrary varieties
• The arc space of a toric variety
• Torification and Factorization of Birational Maps

Related

• The Nash problem from a geometric and topological perspective
• The monodromy conjecture for zeta functions associated to ideals in dimension two
• Containment results for ideals of various configurations of points in P^N
• The holomorphy conjecture for ideals in dimension two
• Monodromy Filtration and Positivity