On direct images of pluricanonical bundles

نویسندگان

  • Mihnea Popa
  • Christian Schnell
چکیده

We show that techniques inspired by Kollár and Viehweg’s study of weak positivity, combined with vanishing for log-canonical pairs, lead to new generation and vanishing results for direct images of pluricanonical bundles. We formulate the strongest such results as Fujita conjecture-type statements, which are then shown to govern a range of fundamental properties of direct images of pluricanonical and pluriadjoint line bundles, like effective vanishing theorems, weak positivity, or generic vanishing.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Higher Cohomology of the Pluricanonical Bundle Is Not Deformation Invariant

In this paper, we compute the dimensions of the 1st and 2nd cohomology groups of all the anti-pluricanonical bundles for Hirzebruch surfaces, and the dimensions of the 1st and 2nd cohomology groups of the second anti-pluricanonical bundles for a blow-up of a projective plane along finite many distinct points. Both of them give examples showing that the higher cohomology of the pluricanonical bu...

متن کامل

Ja n 20 08 Bergman kernels and the pseudoeffectivity of relative canonical bundles - I -

The main result of the present article is a (practically optimal) criterion for the pseudoeffectivity of the twisted relative canonical bundles of surjective projective maps. Our theorem has several applications in algebraic geometry; to start with, we obtain the natural analytic generalization of some semipositivity results due to E. Viehweg and F. Campana. As a byproduct, we give a simple and...

متن کامل

The Asymptotic Tian-yau-zelditch Expansion on Riemann Surfaces with Constant Curvature

Let M be a regular Riemann surface with a metric which has constant scalar curvature ρ. We give the asymptotic expansion of the sum of the square norm of the sections of the pluricanonical bundles K M . That is, dm−1 X i=0 ‖Si(x0)‖ 2 hm ∼ m(1 + ρ 2m ) +O „

متن کامل

Curvature semipositivity of relative pluricanonical systems

We prove semipositivity of the curvature of the Narashimhan-Simha metric on an arbitrary flat projective family of varieties with only canonical singularities. This also implies that the direct image of pluricanonical systems have natural continuous hermitian strucutres with semipositive curvature curvature currents in the sense of Nakano. This paper is a revised version of [T4] using [T5, T6]....

متن کامل

$PI$-extending modules via nontrivial complex bundles and Abelian endomorphism rings

A module is said to be $PI$-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this paper, we focus on direct summands and indecomposable decompositions of $PI$-extending modules. To this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014