We study singularities f∈ K [[x 1,…, xn]] over an algebraically closed field K of arbitrary
characteristic with respect to right respectively contact equivalence, and we establish that …

AMS :: St. Petersburg Mathematical Journal Skip to Main Content American Mathematical
Society American Mathematical Society MathSciNet Bookstore Publications Publications …

There are no known failures of Bounded Negativity in characteristic 0. In the light of recent
work showing the Bounded Negativity Conjecture fails in positive characteristics for rational …

We consider different notions of non-degeneracy, as introduced by Kouchnirenko (NND),
Wall (INND) and Beelen-Pellikaan (WNND) for plane curve singularities {f (x, y)= 0} and …

A celebrated theorem due to O. Zariski (Ann. of Math. 1939), asserts that if S is an algebraic
surface over a field (algebraically closed and of characteristic zero), one can resolve the …

This dissertation is intended to give a systematic treatment of hypersurface singularities in
arbitrary characteristic which provides the necessary tools, theoretically and …

We construct an explicit deformation of a plane branch with constant δ-invariant, where δ
denotes the double point number of the singularity. The generic fibers of the deformation are …

We study classical and new invariants of plane curve singularities f∈ K [[x, y]], K an
algebraically closed field of characteristic p⩾ 0. It is known, in characteristic zero, that κ (f) …

In this work we deal with dicritical divisors, curvettes and polynomials. These objects have
been one of the main research interests of Abhyankar during his last years. In this work we …

The study of singularities of algebraic or analytic spaces over the field of complex numbers
is a traditional subject, but, in contrast, the parallel theory over arbitrary algebraically closed …