Gergely Bérczi

collaborators

4 papers

math.AG2026

Virtual invariants from the non-associative Hilbert scheme

Gergely BÃ©rczi, 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…

math.AG2026

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

Gergely BÃ©rczi, LÃ¡szlÃ³ M. FehÃ©r

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

math.AG2026

Evolving Ranking Functions for Canonical Blow-Ups in Positive Characteristic

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.CO2026

Flow-based Extremal Mathematical Structure Discovery

The discovery of extremal structures in mathematics requires navigating vast and nonconvex landscapes where analytical methods offer little guidance and brute-force search becomes…