We prove the multivariable Strong Monodromy Conjecture for the local topological zeta function of arbitrary tuples of nonzero nonunit plane curve germs. The entries may be nonreduced and may have common irreducible factors. We also prove that the non-equivariant local motivic and topological zeta functions have the same polar locus and generic pole orders, using a multivariable extension of the Nicaise--Xu definition of motivic pole order. Our arguments combine twisted Poincar\'e residues with resolution formulas and specialization to one variable. In arbitrary dimension, we prove that a nonzero iterated residue class on a stratum of a log resolution implies the vanishing of the Bernstein--Sato ideal at the corresponding parameter. In particular, every topological polar hyperplane whose order equals the ambient dimension is contained in this zero locus. For algebraic germs, the topological pole order is at most the motivic pole order, and the two attain maximal order simultaneously.
We prove the strong local monodromy conjecture for poles of order at least $n-1$ of the naive motivic zeta-function for a complex polynomial of $n$ variables. Moreover, for every such pole $s$, we construct an explicit homology $\exp(2\pi i s)$-eigencycle in a neighborhood of any given 1-dimensional exceptional stratum...
We study numerical comparisons for hypersurface singularities under finite holomorphic maps between smooth germs. We retain Jelonek's topological proof of the Milnor-number inequality in the isolated case and give an algebraic proof using a cyclic factorization, Brieskorn modules, and trace. For a reduced divisor-theor...
Z. Jelonek, V. J. Jorge Pérez, R. A. D. dos Santos· 0 citations
We prove the automorphic commutator relation conjectured by Liu and Wang arXiv:2504.00275, which is the geometric input for the automorphic Clifford relations in their framework relating higher period integrals to higher derivatives of $L$-functions over function fields. The relation was previously established only und...
We prove the Tate conjecture in every codimension on every power of an abelian variety of dimension at most four over a finite field. For geometrically simple fourfolds, we use Broe's theorem and the classification of Frobenius relations. For dihedral pairs of abelian surfaces, we construct algebraic classes using fami...
We compute the orbifold Euler characteristics of strata of $k$-differentials on the moduli space of smooth pointed curves. Our main result is a closed coefficient-extraction formula in terms of hyperbolic functions, valid for arbitrary strata and generalizing the Harer--Zagier formula for the Euler characteristic of th...
Matteo Costantini, A. Giacchetto, Martin Moller et al.· 0 citations
We prove categorical Torelli theorems for ordinary and weighted hypersurfaces using the singularity category of the completed affine cone. For Fano hypersurfaces we use the Kuznetsov component, whereas for hypersurfaces of general type we use the full category of graded matrix factorizations. When the degree is coprime...
