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Determinacy of Determinantal Varieties
Imran Ahmed, Maria Aparecida Soares Ruas
A more general class than complete intersection singularities is the class of determinantal singularities. They are defined by the vanishing of all the minors of a certain size of…
Invariants of Topological Relative Right Equivalences
Imran Ahmed, Maria Aparecida Soares Ruas, João Nivaldo Tomazella
The constancy of the Milnor number has several characterizations which were summarized by Greuel in 1986. This paper presents a study of these characterizations in the case of fami…
Invariants of Relative Right and Contact Equivalences
Imran Ahmed, Maria Aparecida Soares Ruas
We study holomorphic function germs under equivalence relations that preserve an analytic variety. We show that two quasihomogeneous polynomials, not necessarily with isolated sing…
Weighted Homogeneous Polynomials with Isomorphic Milnor Algebras
Imran Ahmed
We recall first some basic facts on weighted homogeneous functions and filtrations in the ring of formal power series. We introduce next their analogues for weighted homogeneou…
Homogeneous Polynomials with Isomorphic Milnor Algebras
Imran Ahmed
In Theorem 3.2 we show that two homogeneous polynomials and having isomorphic Milnor algebras are right-equivalent.
Polar Cremona Transformations and Monodromy of Polynomials
Imran Ahmed
Consider the gradient map associated to any non-constant homogeneous polynomial $f\in \C[x_0,...,x_n]$ of degree , defined by \[ϕ_f=grad(f): D(f)\to \CP^n, (x_0:...:x_n)\to (f_0…