Gergely Bérczi

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math.AG2026

Positivity in classical enumerative geometry: a case study in synchronized AI-assisted mathematics

Gergely Bérczi, László M. Fehér

We study the symmetric polynomial $\prod_{α \in A_{n, d}} (1 + α_{1} x_{1} + \dots + α_{n} x_{n})$ where $A_{n, d} := {α \in Z_{\geq 0}^{n} : ∣ α ∣ = d}$ , which is the total Chern class of…

math.AG2026

Evolving Ranking Functions for Canonical Blow-Ups in Positive Characteristic

Gergely Bérczi

Resolution of singularities in positive characteristic remains a long-standing open problem in algebraic geometry. In characteristic zero, the problem was solved by Hironaka in 196…

math.AG2025

Virtual invariants from the non-associative Hilbert scheme

Gergely Bérczi, Felix Minddal

We introduce a non-associative model for the Hilbert scheme of points in arbitrary dimension. We define a smooth ambient space, which we call the non-associative Hilbert scheme, co…