Author

Alexander Esterov

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Preprint Sep 2026

Whitney fold and cusp for algebraic surfaces, and singularities of discriminants

We describe transversal singularity types of the singular locus of the $A$-discriminant for $A\subset\mathbb Z$, and deduce a Whitney type theorem for a coordinate projection of a surface defined by a general polynomial equation with a given Newton polytope $N$: under mild combinaorial conditions on $N$, all multisingu...

Alexander Esterov, L. Vladimirov, Aliaksandr Yuran · 0 citations

Preprint Oct 2026

The monodromy conjecture for high order poles, and norms of residue antiderivatives

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...

Alexander Esterov · 0 citations