A remark on the Chisini conjecture

TL;DR

This paper proves the Chisini conjecture for generic ramified coverings of degree at least 12 over the complex projective plane, establishing uniqueness based on the branch curve, building upon Kulikov's prior work.

Contribution

The paper extends the proof of the Chisini conjecture to degree 12, improving previous results and confirming the conjecture's validity in this range.

Findings

Proves the Chisini conjecture for degree ≥ 12

Confirms uniqueness of coverings from branch curves in this degree range

Builds upon Kulikov's earlier work to extend the proof

Abstract

The Chisini conjecture asserts that a generic ramified covering over the complex projective plane of degree at least 5 is uniquely determined by its branch curve. We prove this for degree at least 12 using the work of Kulikov (math-AG/9803144).