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You are here: FRIAS Fellows Fellows 2021/22 Dr. Giancarlo Urzúa

Dr. Giancarlo Urzúa

Pontificia Universidad Católica de Chile
Mathematics / Algebraic Geometry

External Senior Fellow (Marie S. Curie FCFP)
September 2023 - December 2023


Giancarlo Urzúa received his Licenciatura and Magister en Matemáticas at UC Chile during 1997-2003. Under a Fulbright-CONICYT fellowship, he obtained his Ph.D. in Mathematics in 2008 at the University of Michigan, USA. Between 2008 and 2011 he was a visiting assistant professor at the University of Massachusetts at Amherst, USA. He joined the faculty of UC Chile in 2011. His long-term research visits include Max Planck Institute at Bonn (2010), Korea Institute for Advanced Study at Seoul (2015 and 2023), University of Massachusetts at Amherst (2016), Center of Mathematics at University of Porto (2019), MFO Oberwolfach (2022).

Selected Publications

  • Categorical aspects of the Kollár–Shepherd-Barron correspondence (with J. Tevelev), arXiv: 2204.13225, submitted.
  • Savage surfaces (with S. Troncoso), arXiv:1912.07378, to appear in the Journal of the E.M.S. (2022).
  • Chern slopes of simply connected complex surfaces of general type are dense in [2,3] (with X. Roulleau), Annals of Mathematics (2) 182(2015), 287–306.
  • Flipping surfaces (with P. Hacking and J. Tevelev), J. Algebraic Geom. 26(2017), 279-345.
  • Arrangements of curves and algebraic surfaces, J. Algebraic Geom. 19(2010), 243–284.

FRIAS Research Project

Categorical and Geometrical Aspects of Algebraic Surfaces

Our project aims for a better understanding of algebraic surfaces and their deformations by means of modern tools and points of view such as semi-orthogonal decompositions of derived categories, birational geometry, and moduli spaces. The idea is to consolidate the new lines of research that have emerged from our recent works. The motivation comes from current questions in the very active area of derived categories of algebraic varieties and their deformations, and from classical questions about complex surfaces. We work on three main interconnected lines of research: the geometry of surfaces in degenerations from semi-orthogonal decompositions, topological aspects from the generalized Coble-Mukai lattice, and configurations of rational curves and exotic 4-manifolds.