Displaying similar documents to “Newton's methods from a geometric point of view.”

Indices of 1-forms and Newton polyhedra.

Alexander Esterov (2005)

Revista Matemática Complutense

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A formula of Matsuo Oka (1990) expresses the Milnor number of a germ of a complex analytic map with a generic principal part in terms of the Newton polyhedra of the components of the map. In this paper this formula is generalized to the case of the index of a 1-form on a local complete intersection singularity (Theorem 1.10, Corollaries 1.11, 4.1). In particular, the Newton polyhedron of a 1-form is defined (Definition 1.6). This also simplifies the Oka formula in some particular cases...

Note on the Newton number.

Gwoździewicz, Janusz (2008)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Generic Newton polygons of Ekedahl-Oort strata: Oort’s conjecture

Shushi Harashita (2010)

Annales de l’institut Fourier

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We study the moduli space of principally polarized abelian varieties in positive characteristic. In this paper we determine the Newton polygon of any generic point of each Ekedahl-Oort stratum, by proving Oort’s conjecture on intersections of Newton polygon strata and Ekedahl-Oort strata. This result tells us a combinatorial algorithm determining the optimal upper bound of the Newton polygons of principally polarized abelian varieties with a given isomorphism type of p -kernel. ...