Publications by Alejandro Melle Hernández

Published Articles in Preprint Form

(Reprints of definitive published versions available upon request)

On the pre-lambda ring structure on the Grothendieck ring of stacks and the power structures over it to appear in Bulletin London Mathematical Society, (with Sabir M. Gusein-Zade and Ignacio Luengo).
Linear systems associated to unicuspidal rational plane curves , to appear in Osaka Journal of Mathematics, (with Daniel Daigle).
On Quasi-Ordinary Singularities and Newton Trees , Moscow Mathematical Journal, 2013, v.13, (with Enrique Artal-Bartolo, Pierrette Cassou-Noguès and Ignacio Luengo).
Linear systems of rational curves on rational surfaces , Moscow Mathematical Journal, 2012, v.12, no. 2, 261-268, (with Daniel Daigle).
On piecewise isomorphism of some varieties Azerbaijan Journal of Mathematics 1 (2011), no. 2, 7 pp. (with Sabir M. Gusein-Zade and Ignacio Luengo).
On nu-Quasi-Ordinary Power Series: Factorization, Newton Trees and Resultants , Topology of Algebraic Varieties and Singularities. Edited by José Ignacio Cogolludo-Agustín, Universidad de Zaragoza, and Eriko Hironaka, Florida State University. This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held June 22-26, 2009, in Jaca, Spain. Contemporary Mathematics, 538. American Mathematical Society, Providence, RI, 2011. pp. 321-344. ISBN: 978-0-8218-4890-6, (with Enrique Artal-Bartolo, Pierrette Cassou-Noguès and Ignacio Luengo).
On Generating Series of Classes of Equivariant Hilbert Schemes of Fat Points Moscow Mathematical Journal, 2010, v.10, 593-602, (with Sabir M. Gusein-Zade and Ignacio Luengo).
On a conjecture by A. Durfee Real and Complex Singularities, Edited by M. Manoel (Universidade de Sao Paulo), M. C. Romero Fuster (Universitat de Valéncia, Spain), C. T. C. Wall (University of Liverpool), London Mathematical Society Lecture Note Series (No. 380), ISBN: 9780521169691, October 2010, 416 pages, 1-16, (with Enrique Artal-Bartolo and Jorge Carmona Rúber).
Milnor Number of Weighted-Lê-Yomdin Singularities International Mathematical Research Notices, (2010) Vol. 2010, 4301-4318; first published online March 14, 2010 doi:10.1093/imrn/rnq041 (with Enrique Artal-Bartolo, Javier Fernández de Bobadilla and Ignacio Luengo).
Monodromy Jordan blocks, b-functions and poles of zeta functions for germs of plane curves Journal of Algebra, 324, 2010, 1364-1382, (with Tristán Torrelli and Wim Veys).
Generating series of classes of Hilbert schemes of points on orbifolds Proceedings of the Steklov Institute of Mathematics, v.267, 2009, 125-130, (with Sabir M. Gusein-Zade and Ignacio Luengo).
On maximal poles of zeta functions, roots of b-functions and monodromy Jordan blocks Journal of Topology, 2, (2009) 517-526. doi:10.1112/jtopol/jtp021, (with Tristán Torrelli and Wim Veys).
On the log-canonical threshold for germs of plane curves , Singularities I. Algebraic and analytic aspects. Proceedings of the International School and Workshop on the Geometry and Topology of Singularities held in honor of the 60th birthday of Lê Dung Tráng in Cuernavaca, January 8--26, 2007. Edited by Jean-Paul Brasselet, José Luis Cisneros-Molina, David Massey, José Seade and Bernard Teissier. Contemporary Mathematics, 474. American Mathematical Society, Providence, RI, 2008. pp. 1--14. ISBN: 978-0-8218-4458-8, (with Enrique Artal-Bartolo, Pierrette Cassou-Noguès and Ignacio Luengo).
An equivariant version of the monodromy zeta-function Geometry, Topology, and Mathematical Physics: S. P. Novikov's Seminar: 2006-2007 - V. M. Buchstaber, Steklov Institute of Mathematics, and I. M. Krichever, Columbia University, Editors Advances in the Mathematical Sciences, Translations Series 2, volume 224, AMS, 2008, pp. 139--146. ISBN-10: 0-8218-4674-4, (with Sabir M. Gusein-Zade and Ignacio Luengo).
On the power structure over the Grothendieck ring of varieties and its applications Proceedings of the Steklov Institute of Mathematics, 258 (2007), 58--69. ISBN: 978-5-02-036672-5; 978-5-02-035888-1, (with Sabir M. Gusein-Zade and Ignacio Luengo).
On Rational Cuspidal Plane Curves, Open Surfaces and Local Singularities , SINGULARITY THEORY, Dedicated to Jean-Paul Brasselet on His 60th Birthday, Proceedings of the 2005 Marseille Singularity School and Conference CIRM, Marseille, France 24 January - 25 February 2005, edited by Denis Chèniot, Nicolas Dutertre, Claudio Murolo, David Trotman and Anne Pichon, 2007, pag. 411-442, (with Javier Fernández de Bobadilla, Ignacio Luengo and András Némethi).
Classification of Rational Unicuspidal Projective Curves whose Singularities Have one Puiseux Pair , Real and Complex Singularities, Sao Carlos Workshop in Marseille, 2004, Editors Jean-Paul Brasselet and María Aparecida Soares Ruas, Trends in Mathematics, Birhäuser, 2006, p. 31-45, ISBN 978-3-7643-7775-5, (with Javier Fernández de Bobadilla, Ignacio Luengo and András Némethi).
Integration over spaces of non-parametrized arcs and motivic versions of the monodromy zeta function Proceedings of the Steklov Institute of Mathematics, 252, (2006) 63--73, (with Sabir M. Gusein-Zade and Ignacio Luengo).
Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points Michigan Mathematical Journal Volume 54, (2006) Issue 2 353-359, (with Sabir M. Gusein-Zade and Ignacio Luengo).
Superisolated surface singularities , Singularities and computer algebra, London Math. Soc. Lecture Note Ser., 324, Cambridge Univ. Press, Cambridge, 2006, 13--39. ISBN: 0521683092, (with Enrique Artal-Bartolo and Ignacio Luengo).
On rational cuspidal projective plane curves , Proceedings London Math. Soc. (3), 92, (2006), no. 1, 99-138, (with Javier Fernández de Bobadilla, Ignacio Luengo and András Némethi).
Quasi-ordinary singularities and their zeta functions , Memoirs of the American Mathematical Society, Number 841, volume 178, November 2005, ISSN 0065-9255. 92 pp, (with Enrique Artal-Bartolo, Pierrette Cassou-Noguès and Ignacio Luengo).
Links and analytic invariants of superisolated singularitiess , Journal of Algebraic Geometry. 14, no. 3, (2005), 543-565, (with Ignacio Luengo and András Némethi).
A power structure over the Grothendieck ring of varieties, Mathematical Research Letters, 118, (2004), 261-278, (with Sabir M. Gusein-Zade and Ignacio Luengo).
Monodromy Conjecture for some surface singularities , Annales Scientifiques de l'École Normale Supérieure, Vol 35, (2002), pp. 605-640, (with Enrique Artal-Bartolo, Pierrette Cassou-Noguès and Ignacio Luengo).
Denef-Loeser zeta function is not a topological invariant Journal of the London Mathematical Society, 65, (2002), 45-54, (with Enrique Artal-Bartolo, Pierrette Cassou-Noguès and Ignacio Luengo).
Pencils of curves on smooth surfaces , Proceedings of the London Mathematical Society, (3), 83 (2001), 257-278, (with Terry Wall).
Bifurcations and topology of meromorphic germs New developments in singularity theory, Isaac Newton Institute in Cambridge, (2000), NATO Sci. Ser. II Math. Phys. Chem., 21, Editores: D. Siersma, C.T.C. Wall, V. Zakalyukin. Kluwer Academic Publishers, Dordrecht. pp. 279--304, 2001, (with Sabir M. Gusein-Zade and Ignacio Luengo).
On a conjecture of W. Veys Mathematische Annalen, 317, (2000), 325-327, (with Enrique Artal-Bartolo and Ignacio Luengo).
On the zeta function of a polynomial at infinity Bull. Sci. Math. 124, no. 3 (2000), 213-224, (with Sabir M. Gusein-Zade and Ignacio Luengo).
Milnor number at infinity, topology and Newton boundary of a polynomial function Mathematische Zeitschrift, 233, (2000), 679-696, (with Enrique Artal-Bartolo and Ignacio Luengo).
On the topology of a generic fibre of a polynomial map Comm. in Algebra, 28, (2000), 1767-1787, (with Enrique Artal-Bartolo and Ignacio Luengo).
On polar invariants of hypersurface singularities. Annales de la Facultè des Sci. de Toulouse 6, (2000), 671-688.
Milnor numbers for surface singularities Israel Journal of Mathematics, 115, (2000), 29-50.
Topology of meromorphic germs and its aplications Algebra i Analiz. {11}, no. 5 (1999), 775--780. Tranlated in St. Petersburg Math. J. {11} (2000), 775-780, (with Sabir M. Gusein-Zade and Ignacio Luengo).
On the topology of germs of meromorphic functions Firat Üniversitesi Fen ve Müh. Bilimleri Dergisi (Journal of Science and Engineering), 11, no. 3 (1999), 121--132, (with Sabir M. Gusein-Zade and Ignacio Luengo).
On atypical values and local monodromies of meromorphic functions. Solitons, Geometry and Topology: on the Crossroads: Collection of Papers Dedicated to the 60th Anniversary of Academician S.P. Novikov. en Proceedings of the Steklov Institute of Mathematics, 225 (1999), 3168-3176, (with Sabir M. Gusein-Zade and Ignacio Luengo).
Euler characteristic of the Milnor fibre of plane singularities, Proc. Amer. Math. Soc., 127 (1999), 2653-2655.
Zeta-functions for germs of meromorphic functions and Newton diagrams Funct. Anal. and its Appl. 32, no. 2 (1998), 93-99, (with Sabir M. Gusein-Zade and Ignacio Luengo).
Partial resolutions and the zeta-function of a singularity Comment. Math. Helv. {72}, n. 2 (1997), 244--256, (with Sabir M. Gusein-Zade and Ignacio Luengo).
A formula for the Milnor number C.R. Acad. Sci. Paris Sec. 1 Mathématiques, 321, (1995), 1473-1478, (with Ignacio Luengo).
Topología de singularidades de hipersuperficies: número de Milnor e invariantes polares, Tesis Doctoral. Facultad de Matemáticas, Universidad Complutense de Madrid, defendida 21/05/1996.

Home Alejandro Melle Hernández