"Examples first:"

Consider so(3,C). (Co)Adjoint Orbits can be described by equations 
x^2+y^2+z^2 = R.

R=0 - is nilpotent cone - algebraic closure of the orbit of nilpotent element. (It is union of two orbits - {0} and {Cone w/o {0}} ).

R$\ne$ 0 are orbits of semi-simple elements.
So we have degeneration R->0 - semi-simple orbit degenerates to nilpotent.

**Question** Is there similar description for the other nilpotent orbits in higher dimensions e.g.  for gl(n,c) ? I mean can we write some equations depending on parameters F_t(g)=0,
such that for general "t" we get semi-simple orbits, but for specific values we have nilpotent orbit (more precisely their closures)? (Here "t" can be vector and F is vector-valued algebraic function).

Of course this can be done the  biggest orbit - for nilpotent cone itself.

Consider matrices "M" which satisfy the condition, that 
their characterestic polynom is fixed with values eigs $a_i$:

$det(M-x) = (x-a_1)(x-a_2)...(x-a_n)$


For $a_i$ generic - this is semisimple orbit, but if $a_i = 0$ we get nilpotent cone.

**Question Reformulated** Is it possible to do the same for smaller dimensional orbits ?

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As far as I heard nilpotent orbits can be described by the equations on their rank and 
$M^l=0$, however this does not seems to answer the question.

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Part of motivation for asking  is related to the following questions:

http://mathoverflow.net/questions/83926/on-an-affine-analogue-of-the-fact-mathbbc-mathfrakgg-is-a-polynomial-ri

http://mathoverflow.net/questions/84317/primitive-ideals-of-the-universal-enveloping-algebras-of-affine-lie-algebras

In particular if the answer would be YES - then probably we can do the same in the
"affine case" so answering the question "What replaces the concept of the nilpotent orbit in that case?"