A central issue in defining relative GW-invariants on a symplectic manifold is the possibility that a sequence of relative pseudoholomorphic curves can degenerate in such a manner, that components lie completely in the relative hypersurface V.

This issue is addressed directly by Ionel-Parker in their paper on relative GW-invarianst and also by Li-Ruan in their virtual neighborhood construction. Both come to the conclusion, that after a generic choice of almost complex structure, such behavior can be ruled out.

However, in a preprint (arXiv:0809.3534 ) by McDuff the issue arises again, and she produces an example where is appears that such a degenerate curve has non-expected dimension. Moreover, she states a criterion for the exclusion of such higher level curves in genus 0.

Is McDuff attempting to illustrate an issue not related to the general defintion of relative GW-invariants, or is there an oversight in the papers defining relative GW-invariants?