Newton nondegenerate singularities, the geometric genus and the Seiberg--Witten invariant

Resumen:

In the first half, we define computation sequences and prove some 
properties. Then we calculate the geometric genus and Seiberg--Witten
invariant for Newton nondegenerate hypersurface surface singularities
with rational homology link sphere, using a computation sequence. As a
corollary, the Seiberg--Witten invariant conjecture (to which there are
counterexamples) holds for this class of singularities.

In the second half, we consider generalizations of Newton nondegenerate 
singularities, and show some new formulas for some analytic invariants, 
including the geometric genus. This is work in progress, and we have not 
yet proven a generalization of the formula for the Seiberg--Witten 

invariant.

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