  We show how one may sometimes perform singular ambient surgery on the complex
locus of a real algebraic curve and obtain what we call a floppy curve. A
floppy curve is a certain kind of singular surface in CP(2), more general than
the complex locus of a real nodal curve. We derive analogs for floppy curves of
known restrictions on real nodal curves. In particular we derive analogs of
Fielder's congruence for certain nonsingular curves and Viro's inequalities for
nodal curves which generalize those of Arnold and Petrovskii for nonsingular
curves. We also obtain a determinant condition for certain curves which are
extremal with respect to some of these equalities. One may prohibit certain
schemes for real algebraic curves by prohibiting the floppy curves which result
from singular ambient surgery. In this way, we give a new proof of Shustin's
prohibition of the scheme $1<2\coprod 1<18>>$ for a real algebraic curve of
degree eight.
