93 citations · 274 across the 46 of their papers we have counts for
58 papers
Singularities of rational maps: foundations and surfaces
Caucher Birkar
We develop a theory of singularities of rational maps, focusing on maps and using their polarised graphs and normalised polarised graphs…
Stein degree of proper morphisms
Caucher Birkar
The notion of degree begins in field theory as the dimension of a field extension. In algebraic geometry, this idea reappears as the degree of a finite morphism, defined using the…
Sheaf stable pairs on projective surfaces and birational geometry
Caucher Birkar, Jia Jia, Artan Sheshmani +1
We study moduli space of higher rank marginally stable pairs (E,s:= (s_1,..., s_r)) consisting of torsion free coherent sheaf E of rank r and r sections (s_1,..., s_r) on a smooth…
Toroidal and toric models of fibrations over curves
Caucher Birkar
We construct relatively bounded toroidal and toric models of relatively bounded fibrations over curves.
Stein degree on log Calabi-Yau fibrations
Caucher Birkar, Santai Qu
We prove a conjecture proposed by the first author on boundedness of Stein degree of divisors on log Calabi-Yau fibrations. More precisely, for and ,…
Stein degree on non-Fano type fibrations
Caucher Birkar, Santai Qu
We construct examples showing that Stein degree of vertical divisors on non-Fano type log Calabi-Yau fibrations is unbounded.