11 papers
Irrationality of degenerations of Fano varieties
Caucher Birkar, Santai Qu
In this paper we investigate the degrees of irrationality of degenerations of -lc Fano varieties of arbitrary dimensions. We show that given a generically -lc klt Fano fibr…
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…
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 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.
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…
Singularities on Fano fibrations and beyond
Caucher Birkar
In this paper, we investigate singularities on fibrations and related topics. We prove conjectures of McKernan and Shokurov on singularities on Fano type fibrations and a conjectur…