Addendum to `Fake Projective Planes'

TL;DR

This paper updates and completes the classification of fake projective planes, confirming there are exactly 100 such complex surfaces up to biholomorphism, building on previous foundational work.

Contribution

It provides an updated, corrected, and complete classification of fake projective planes, including recent collaborations that finalize the list of all 100 known cases.

Findings

Classified fake projective planes into 26 classes

Confirmed total of 100 fake projective planes up to biholomorphism

Updated previous results with new corrections and additions

Abstract

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.