Martí Lahoz

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Contact:
Martí Lahoz Vilalta
marti.lahoz[arroba]ub.edu
http://www.ub.edu/geomap/lahoz/

+34 93 402 16 08

Current Position

I am Professor Titular at the Departament de Matemàtiques i Informàtica of the Universitat de Barcelona (UB).
I am Principal Researcher (IP) of the project BIGGAMES.

Research lines

My field of research is Algebraic Geometry. Especially I focus on the applications of abstract homological algebra constructions to the geometry of complex projective varieties.

Publications & Preprints

  1. M. Lahoz, J.C. Naranjo, A. Rojas, and I. Spelta, Monodromy of the Prym map and semicanonical pencils in genus 6. Preprint. [arXiv]
  2. M. Lahoz, J.C. Naranjo, and A. Rojas, Geometry of Prym semicanonical pencils and an application to cubic threefolds. Preprint. [arXiv] [Journal]
  3. M. Lahoz and A. Rojas, Chern degree functions. Commun. Contemp. Math. 25 (2023), no. 5, Paper No. 2250007, 53 pp. [arXiv] [Journal]
  4. F. Caucci and M. Lahoz, Stability of syzygy bundles on abelian varieties. Bull. Lond. Math. Soc. 53 (2021), no. 4, 1030–1036. [arXiv] [Journal]
  5. A. Bayer, M. Lahoz, E. Macrì, H. Nuer, A. Perry, and P. Stellari, Stability conditions in families. Publ. Math. Inst. Hautes Études Sci. 133 (2021), 157–325. [arXiv] [Journal]
  6. A. Bayer, M. Lahoz, E. Macrì, and P. Stellari, Stability conditions on Kuznetsov components. Appendix about the Torelli theorem for cubic fourfolds by A. Bayer, M. Lahoz, E. Macrì, P. Stellari, and X. Zhao. To appear at Ann. Sci. École Norm. Sup. (4). [arXiv] [Journal]
  7. M. Lahoz, M. Lehn, E. Macrì, and P. Stellari, Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects. J. Math. Pures Appl. (9) 114 (2018), 85–117 [Journal] [arXiv]
  8. O. Debarre, Z. Jiang, and M. Lahoz, with an Appendix by W. Sawin. Rational cohomology tori. Geom. Topol. 21 (2017), no. 2, 1095–1130. [Journal] [arXiv]
  9. M. Gulbrandsen and M. Lahoz, Schottky via the punctual Hilbert scheme. Tohoku Math. J. (2) 69, no. 4 (2017), 611--619. [Journal] [arXiv]
  10. M. Lahoz, E. Macrì, and P. Stellari, Arithmetically Cohen–Macaulay bundles on cubic fourfolds containing a plane. Brauer Groups and Obstruction Problems. Volume 320 of the series Progress in Mathematics, 155–175. Birkhäuser/Springer, Cham, 2017. [Journal] [arXiv]
  11. M. Lahoz, E. Macrì, and P. Stellari, Arithmetically Cohen–Macaulay bundles on cubic threefolds. Algebr. Geom. 2 (2015), no. 2, 231–269. [Journal] [arXiv]
  12. Z. Jiang, M. Lahoz, and S. Tirabassi, Characterization of products of theta divisors. Compos. Math. 150 (2014), no. 8, 1384–1412. [Journal] [arXiv]
  13. Z. Jiang, M. Lahoz, and S. Tirabassi, On the Iitaka fibration of varieties of maximal Albanese dimension. Int. Math. Res. Not. 2013 (2013), no. 13, 2984–3005. [Journal] [arXiv]
  14. M. Lahoz and J.C. Naranjo, Theta-duality on Prym varieties and a Torelli theorem. Trans. Amer. Math. Soc. 365 (2013), no. 10, 5051–5069. [Journal] [arXiv]
  15. M. Lahoz, Generic vanishing index and the birationality of the bicanonical map of irregular varieties. Math. Z., 272, (2012), no. 3-4, 1075–1086. [Journal] [arXiv]
  16. M.A. Barja, M. Lahoz, J.C. Naranjo, and G. Pareschi, On the bicanonical map of irregular varieties. J. Algebraic Geom. 21 (2012), no.3, 445–471. [Journal] [arXiv]
  17. M. Gulbrandsen and M. Lahoz, Finite subschemes of abelian varieties and the Schottky problem. Ann. Inst. Fourier, 61 (2011), no. 5, 2039–2064. [Journal] [arXiv]
  18. S. Casalaina-Martin, M. Lahoz, and F. Viviani, Cohomological support loci for Abel-Prym curves. Matematiche 63 (2008), no. 1, 205–222. [Journal] [arXiv]

Events Co-organized

November 2023
Workshop Mediterranean Algebraic Geometry Seminar. Séminaire Méditerranéen de Géométrie Algébrique. [webpage] UB, Barcelona, Spain.
November 2020
Workshop Mediterranean Algebraic Geometry Seminar. Séminaire Méditerranéen de Géométrie Algébrique. [webpage] CIRM, Luminy, France.
April 2018
Workshop Sheaves, curves, and moduli. [webpage] University of Stavanger, Norway.
May 2017
Spring School Positivity in Arithmetic and Geometry. [webpage] Université Paris-Sud, Orsay, France.
June 2016
Summer School and Conference New Methods in Birational Geometry. [webpage] Toulouse, France.
June 2016
Nordfjordeid Summer School Stability conditions on triangulated categories and geometric applications. [webpage] Sophus Lie Conference Center, Nordfjordeid, Norway.
September 2015
Workshop Derived Categories and Moduli Spaces. [webpage] Stavanger, Norway.
May 2013
Summer School Compactifying Moduli Spaces. [webpage] Barcelona, Spain.
Notes by Valery Alexeev: Moduli of Weighted Hyperplane Arrangements, Birkhäuser, 2015.
Notes by Paul Hacking, Radu Laza and Dragos Oprea: Compactifying Moduli Spaces, Birkhäuser, 2016.
July 2012
Short Summer School The derived category of cubic hypersurfaces. [webpage] Barcelona, Spain.












Previous Positions



2017 - 2022
Ramón y Cajal researcher (RyC) at the Departament de Matemàtiques i Informàtica of the Universitat de Barcelona (UB).
2013 - 2017
Maître de Conférences (MdC) of the UFR en Mathématiques of the Université Paris Diderot - Paris 7, where I was member of the project "Topologie et géométrie algébrique" (TGA) of the "Institut de Mathematiques de Jussieu - Paris Rive Gauche" (IMJ-PRG – UMR7586).
2012 - 2013
Sophie Germain postdoc at the AGA research group of the "Département de Mathématiques d'Orsay" (UMR8628) of the Université Paris Sud 11.
2010 - 2012
SFB TR 45 postdoc at the "Mathematisches Institut" of the Universität Bonn.
2008 - 2010
Professor ajudant at the "Departament d'Àlgebra i Geometria" of the Universitat de Barcelona.
2005 - 2008
Becario FPU at the "Departament de Matemàtica Aplicada 1" of the Universitat Politècnica de Catalunya.







Long Research Visits

Apr - May 2015
IMPA, Rio de Janeiro (Brasil). 5 weeks.
Special Thematic Program on Algebraic Geometry
Feb - Mar 2012
The Ohio State University, Columbus, Ohio (USA). 4 weeks.
Host: E. Macrì. Related topic: Derived category of cubic hypersurfaces.
Sept - Dec 2007
Università degli Studi di Roma, "Tor Vergata", Roma (Italy). 17 weeks.
Tutor: G. Pareschi. Related topic: Bicanonical Map on Irregular Varieties.
Oct - Dec 2006
Università degli Studi di Roma, "Tor Vergata", Roma (Italy). 10 weeks.
Tutor: G. Pareschi. Related topic: Castelnuovo Theory on Abelian Varieties.








Education

May 2010
Doctor (PhD) in Mathematics, algebraic geometry (UPC).
Title dissertation: Theta-duality in Abelian Varieties and the Bicanonical Map of Irregular Varieties.
Doctorate Extraordinary Award.
1999-2004
Llicenciatura (BSc) in Mathematics (UPC).