Geodesic
Newton polyhedra (resolution of singularities)
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki", Tome 22 (1983), pp. 207-239
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Some results are presented on the resolution of singularities and compactification of an algebraic manifold determined by a system of algebraic equations with fixed Newton polyhedra and rather general coefficients. Resolution and compactification are carried out by means of smooth toric manifolds which are described in the first half of the survey. 
@article{INTD_1983_22_a5,
     author = {A. G. Khovanskii},
     title = {Newton polyhedra (resolution of singularities)},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {207--239},
     year = {1983},
     volume = {22},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1983_22_a5/}
}
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A. G. Khovanskii. Newton polyhedra (resolution of singularities). Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki", Tome 22 (1983), pp. 207-239. http://geodesic.mathdoc.fr/item/INTD_1983_22_a5/