3,220 research outputs found
Dicritical divisors after S.S. Abhyankar et I. Luengo
In [AL11], S.S Abhyankar and I. Luengo introduce a new theory of dicritical
divisors in the most general framework. Here we simplify and generalize their
results (see Theorems 3.1 and 3.2)
Singularities in positive characteristic, stratification and simplification of the singular locus
We introduce an upper semi-continuous function that stratifies the highest
multiplicity locus of a hypersurface in arbitrary characteristic (over a
perfect field). The blow-up along the maximum stratum defined by this function
leads to a form of simplification of the singularities, also known as a
reduction to the monomial case.Comment: Several typos corrected. Minor improvements on the presentation of
the published pape
Techniques for the study of singularities with applications to resolution of 2-dimensional schemes
We give an overview of invariants of algebraic singularities over perfect
fields. We then show how they lead to a synthetic proof of embedded resolution
of singularities of 2-dimensional schemes.Comment: 26 pages; minor changes have been adde
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