Let f : (C^n, 0) -->(C, 0) be an analytic function germ. Under the hypothesis that f is
Newton non-degenerate, we compute the \mu*-sequence of f in terms of the Newton
polyhedron of f . This sequence was defined by ...
Bivià-Ausina, Carles; Huarcaya, Jorge A C(Elsevier, 2015-02)
Let F: Kn→Kn be a polynomial map such that F−1(0) is compact, where View the MathML source. Then we give a condition implying that there is a uniform bound for the Łojasiewicz exponent at infinity in certain deformations ...
[EN] Given a pair of monomial ideals $I$ and $J$
of finite colength of the ring of analytic function germs $(\C^n,0)\to \C$, we prove that
some power of $I$ admits a reduction formed by homogeneous polynomials with respect ...
Bivià-Ausina, Carles; Fukui, Toshizumi(Oxford University Press, 2017)
[EN] We introduce the notion of bi-Lipschitz equivalence of ideals and derive numerical invariants for such equivalence. In particular, we show that the log canonical threshold of ideals is a bi-Lipschitz invariant. We ...
[EN] We characterize the ideals I of On of finite colength whose integral closure is equal to the integral closure of an ideal generated by pure monomials. This characterization, which is motivated by an inequality proven ...
We give an expression for the Lojasiewicz exponent of a wide class of n-tuples of ideals (I (1),aEuro broken vertical bar,I (n) ) in using the information given by a fixed Newton filtration. In order to obtain this expression ...
Bivià-Ausina, Carles; Ruas, M.A.S.(Cambridge University Press, 2020-05)
[EN] We extend the notions of mu*- sequences and Tjurina numbers of functions to the framework of Bruce-Roberts numbers, that is, to pairs formed by the germ at 0 of a complex analytic variety X. Cn and a finitely R( ...
We study the Lojasiewicz exponent and the log canonical threshold of ideals of O-n when restricted to generic subspaces of C-n of different dimensions. We obtain effective formulas of the resulting numbers for ideals with ...
Bivià-Ausina, Carles(Cambridge University Press (CUP) + Australian Mathematical Publishing Association Inc., 2015-04)
We obtain a characterisation of the monomial ideals I subset of C[x(1), . . . , x(n)] of finite colength that satisfy the condition e(I) = L-0((1)) (I) . . . L-0((n)) (I), where L-0((1)) (I), . . . , L-0((n)) (I) is the ...
Bivià-Ausina, Carles; Huarcaya, Jorge Alberto C.(Springer-Verlag, 2019-03)
[EN] In this article we characterize the polynomialmaps F : Cn. Cn for which F -1(0) is finite and their multiplicity mu(F) is equal to n! Vn( +(F)), where +(F) is the global Newton polyhedron of F. As an application, we ...
We give an expression for the Lojasiewicz exponent of a set of ideals which are pieces of a weighted homogeneous filtration We also study the application of this formula to the computation of the Lojasiewicz exponent of ...
[EN] We analyze the sequence L-J*(I) of mixed Lojasiewicz exponents attached to any pair I, J of monomial ideals of finite colength of the ring of analytic function germs ((C-n, 0) -> C. In particular, we obtain a combinatorial ...
Bivià-Ausina, Carles; Huarcaya, Jorge Alberto C.(Springer-Verlag, 2017-04)
[EN] Let F : C-n -> C-n be a polynomial map such that F-1 (0) is finite. We analyze the connections between the multiplicity of F, the Newton polyhedron of F and the set of special monomials with respect to F, which is a ...