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 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.