Abstract
The ZamolodchikovW(3)-algebraW(3)(c) with central charge c has full automorphism group Z(2). It was conjectured in the physics literature over 20 years ago that the orbifold (W-3(c))(Z2) is of type W(2, 6, 8, 10, 12) for generic values of c. We prove this conjecture for all c not equal 559 +/- 7 root 76657/95, and we show that for these two values, the orbifold is of typeW(2, 6, 8, 10, 12, 14). This paper is part of a larger program of studying orbifolds and cosets of vertex algebras that depend continuously on a parameter. Minimal strong generating sets for orbifolds and cosets are often easy to find for generic values of the parameter, but determining which values are generic is a difficult problem. In the example of (W-3(c))(Z2), we solve this problem using tools from algebraic geometry.