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Autor Melle Hernández, Alejandro |
Documentos disponibles escritos por este autor (54)
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Melle Hernández, Alejandro ; Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio | Springer | 2006Notions of integration of motivic type over the space of arcs factorized by the natural C*-action and over the space of nonparametrized arcs (branches) are developed. As an application, two motivic versions of the zeta function of the classical [...]![]()
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Given a curve C on a projective nonsingular rational surface S, over an algebraically closed eld of characteristic zero, we are interested in the set C of linear systems L on S satisfying C 2 L, dimL 1, and the general member of L is a rationa[...]![]()
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Luengo Velasco, Ignacio ; Melle Hernández, Alejandro ; Némethi, A. | American Mathematical Society | 2005Using superisolated singularities we present examples and counterexamples to some of the most important conjectures regarding invariants of normal surface singularities. More precisely, we show that the ``Seiberg-Witten invariant conjecture''(of[...]![]()
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In this paper we show that the Euler characteristic of the generic fibre of a complex polynomial function f : C-n --> C can be easily computed using the Newton number of f. We apply this result to study polynomials with a finite number of criti[...]![]()
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An additive formula for the Milnor number of an isolated complex hypersurface singularity is shown. We apply this formula for studying surface singularities. Durfee's conjecture is proved for any absolutely isolated surface and a generalization [...]![]()
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Melle Hernández, Alejandro ; Artal Bartolo, Enrique ; Cassou-Noguès, Pierrette ; Luengo Velasco, Ignacio | Société Mathématique de France | 2002-07In this work we give a formula for the local Denef–Loeser zeta function of a superisolated singularity of hypersurface in terms of the local Denef–Loeser zeta function of the singularities of its tangent cone. We prove the monodromy conjecture f[...]![]()
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We study the poles of several local zeta functions: the Igusa, topological and motivic zeta function associated to a germ of a holomorphic function in two variables. It was known that there is at most one double pole for (any of) these zeta func[...]![]()
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Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Springer | 1999A meromorphic function on a compact complex analytic manifold defines a C? locally trivial bundle over the complement to a finite subset of the projective line CP1, the bifurcation set. The monodromy transformations of this bundle correspond to [...]![]()
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Artal Bartolo, Enrique ; Carmona Ruber, Jorge ; Melle Hernández, Alejandro | Cambridge University Press | 2010This note provides a negative answer to the following question of A. H. Durfee [Invent. Math. 28 (1975), 231–241; ]: Is it true for arbitrary polynomials F(x,y,z) having an isolated singularity at the origin that the local monodromy is of finite[...]![]()
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In this work we show a singular K3 surface S of such that producing a counter-example to a conjecture of Veys.![]()
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Luengo Velasco, Ignacio ; Gusein-Zade, Sabir Medgidovich ; Melle Hernández, Alejandro | Independent University of Moscow | 2010-09We discuss different definitions of equivariant (with respect to an action of a finite group on a manifold) Hilbert schemes of zero-dimensional subschemes and compute generating series of classes of equivariant Hilbert schemes for actions of cyc[...]![]()
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The main objects of this study are the poles of several local zeta functions: the Igusa, topological, and motivic zeta function associated to a polynomial or (germ of) holomorphic function in n variables. We are interested in poles of maximal po[...]![]()
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Gusein-Zade, Sabir Medgidovich ; Luengo Velasco, Ignacio ; Melle Hernández, Alejandro | Azerb. Math. Soc | 2011Two quasi-projective varieties are called piecewise isomorphic if they can be stratified into pairwise isomorphic strata. We show that the m-th symmetric power Sm(Cn) of the complex affine space Cn is piecewise isomorphic to Cmn and the m-th sym[...]