We construct the giant graviton on AdS_{4} x CP^{3} out of a four-brane
embedded in and moving on the complex projective space. This configuration is
dual to the totally anti-symmetric Schur polynomial operator
\chi_{R}(A_{1}B_{1}) in the 2+1-dimensional, N = 6 super Chern-Simons ABJM
theory. We demonstrate that this BPS solution of the D4-brane action is
energetically degenerate with the point graviton solution and initiate a study
of its spectrum of small fluctuations. Although the full computation of this
spectrum proves to be analytically intractable, by perturbing around a "small'"
giant graviton, we find good evidence for a dependence of the spectrum on the
size, \alpha_{0}, of the giant. This is a direct result of the changing shape
of the worldvolume as it grows in size.Comment: 46 pages, 7 figures. Further details added to section 6 - the
solutions to the leading order fluctuation equations and the leading order
spectrum have been obtained - and additional comments added to the
discussion. Additional references added. Mistake in section 2 correcte
