Polynomial interpolation and the Waldschmidt constant of points in projective space

Abstract

We establish Chudnovsky's Conjecture and, more generally, Demailly's Conjecture for any finite set of points in $\mathbb{P}^n_k$, where $k$ is an algebraically closed field of characteristic 0. The key idea of passing to positive characteristic, as well as the broad plan of the proof, was suggested by ChatGPT-5.6 Sol. All mathematical arguments and proofs in this paper were developed, written, and verified by the authors.

Disclosure

“r algebraically closed fields of sufficiently large positive characteristic. In Section 4, we construct the specialization from characteristic zero to positive characteristic and complete the proof of Theorem 1.2. Role of AI in this work. ChatGPT-5.6 Sol was used in this project. In particular, it suggested a positive-characteristic approach to the problem, first proving the desired inequality for affine points in this setting and then passing to characteristic zero by specializati”

PDF page 3

Classification

Proof ideas or individual proof-step assistance

Multiplier

8

Verified

2026-08-23T05:19:42.051218Z

Structural counts