TL;DR
This paper constructs an explicit minimal surface of general type with a canonical degree of 36, confirming a long-standing conjecture that this is the maximum possible value.
Contribution
It provides the first explicit example of a minimal surface of general type achieving the conjectured maximal canonical degree of 36.
Findings
Confirmed the conjecture that the maximal canonical degree is 36.
Constructed an explicit surface with canonical degree 36.
Improved the known maximum from 16 to 36.
Abstract
It has been conjectured that the optimal canonical degree of a minimal surface of general type is 36, from a work in the 70's of Beauville who proved that 36 was an upper bound. The highest canonical degree known for the problem was 16 by Persson in 1978. The purpose of this article is to confirm the conjecture by providing an explicit surface.
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