The Newton tree: geometric interpretation and applications to the motivic zeta function and the log canonical threshold

Let I be an arbitrary ideal in C[[x,y]]. We use the Newton algorithm to compute by induction the motivic zeta function of the ideal, yielding only few poles, associated to the faces of the successive Newton polygons. We associate a minimal Newton tree to I, related to using good coordinates in the Newton algorithm, and show that it has a conceptual geometric interpretation in terms of the log canonical model of I. We also compute the log canonical threshold from a Newton polygon and strengthen Corti's inequalities.Comment: 32 page

Invariants of plane curve singularities and Newton diagrams

We present an intersection-theoretical approach to the invariants of plane curve singularities $\mu$, $\delta$, $r$ related by the Milnor formula $2\delta=\mu+r-1$. Using Newton transformations we give formulae for $\mu$, $\delta$, $r$ which imply planar versions of well-known theorems on nondegenerate singularities

Multivariable Hodge theoretical invariants of germs of plane curves

We describe methods for calculation of polytopes of quasiadjunction for plane curve singularities which are invariants giving a Hodge theoretical refinement of the zero sets of multivariable Alexander polynomials. In particular we identify some hyperplanes on which all polynomials in multivariable Bernstein ideal vanish

Adapting the Core Language Engine to French and Spanish

We describe how substantial domain-independent language-processing systems for French and Spanish were quickly developed by manually adapting an existing English-language system, the SRI Core Language Engine. We explain the adaptation process in detail, and argue that it provides a fairly general recipe for converting a grammar-based system for English into a corresponding one for a Romance language.Comment: 9 pages, aclap.sty; to appear in NLP+IA 96; see also http://www.cam.sri.com