In this article we extend the construction of giant gravitons from
holomorphic surfaces [arXiv:hep-th/0010206] to the ABJM correspondence. We
construct a new class of 1/6-BPS M5-branes wrapping 5-manifolds in S^7/Z_k and
supported by a large angular momentum in the orbifold space. These orbifold
giant gravitons undergo a supersymmetry enhancement to 1/3-BPS and 1/2-BPS
configurations in special cases. The compactification of M-theory on AdS_4 x
S^7/Z_k to type IIA superstring theory on AdS_4 x CP^3 then gives rise to
another new class of 1/6-BPS D4 and NS5-branes wrapping 4 and 5-manifolds in
CP^3. The D4-branes carry a combination of D0-brane charge and angular momentum
in the complex projective space, while the NS5-branes are supported only by
D0-brane charge. Finally, we present a detailed analysis of a one-parameter
family of 1/2-BPS M5-brane orbifold giant gravitons, and their D4 and NS5-brane
CP^3 descendants.Comment: 34 pages; 1 figure; minor revisions; references adde
