Priyankur Chaudhuri
TIFR, Mumbai
October 27, 2022
Abundance-type problems for generalised pairs: In algebraic geometry, abundance-type problems are those that relate numerical properties of a certain Cartier divisor with properties of the associated line bundle (such as global generation or the existence of nonzero sections). In its most basic form, the abundance conjecture (which is one of the central open problems in higher dimensional algebraic geometry) says that if the canonical divisor of a smooth projective variety is nef (i.e. it intersects every curve non-negatively) then some multiple of the canonical line bundle is generated by global sections. In recent years, several abundance-type conjectures have been proposed for generalised pairs. Instead of dealing just with the canonical divisor $K_X$ of a smooth projective variety $X$, (roughly speaking) these concern divisors of the form $K_X+L$ where $L$ is a nef divisor on $X$. In this talk, I will discuss my recent results on generalised abundance , where I extend some classical results of Kawamata and Ambro to the setting of generalised pairs.
TIFR, Mumbai
October 27, 2022
Abundance-type problems for generalised pairs: In algebraic geometry, abundance-type problems are those that relate numerical properties of a certain Cartier divisor with properties of the associated line bundle (such as global generation or the existence of nonzero sections). In its most basic form, the abundance conjecture (which is one of the central open problems in higher dimensional algebraic geometry) says that if the canonical divisor of a smooth projective variety is nef (i.e. it intersects every curve non-negatively) then some multiple of the canonical line bundle is generated by global sections. In recent years, several abundance-type conjectures have been proposed for generalised pairs. Instead of dealing just with the canonical divisor $K_X$ of a smooth projective variety $X$, (roughly speaking) these concern divisors of the form $K_X+L$ where $L$ is a nef divisor on $X$. In this talk, I will discuss my recent results on generalised abundance , where I extend some classical results of Kawamata and Ambro to the setting of generalised pairs.