Global Division of Cohomology Classes via Injectivity Lawrence Ein and Mihnea Popa
نویسنده
چکیده
The aim of this note is to remark that the injectivity theorems of Kollár and EsnaultViehweg can be used to give a quick algebraic proof of a strengthening (by dropping the positivity hypothesis) of the Skoda-type division theorem for global sections of adjoint line bundles vanishing along suitable multiplier ideal sheaves proved in [EL], and to extend this result to higher cohomology classes as well (cf. Theorem 4.1). For global sections, this is a slightly more general statement of the algebraic version of an analytic result of Siu [Siu] based on the original Skoda theorem. In §4 we list a few consequences of this type of result, like the surjectivity of various multiplication or cup-product maps and the corresponding version of the geometric effective Nullstellensatz.
منابع مشابه
Global Division of Cohomology Classes via Injectivity
The aim of this note is to remark that the injectivity theorems of Kollár and EsnaultViehweg can be used to give a quick algebraic proof of a strengthening (by dropping the positivity hypothesis) of the Skoda-type division theorem for global sections of adjoint line bundles vanishing along suitable multiplier ideal sheaves proved in [EL], and to extend this result to higher cohomology classes a...
متن کاملExtension of Sections via Adjoint Ideals Lawrence Ein and Mihnea Popa
We prove some extension theorems and applications, inspired by the very interesting recent results of Hacon-McKernan [HM1], [HM2] and Takayama [Ta], used in the minimal model program and in turn inspired by fundamental results of Siu. Parts of the proofs we give follow quite closely techniques in [Ka], [HM1], [HM2], and [Laz], which use asymptotic constructions. Some related analytic statements...
متن کاملGeneric Vanishing and Minimal Cohomology Classes on Abelian Fivefolds
We classify GV -subschemes of five-dimensional ppavs, proving the main conjecture in [PP08b] in this case. This result is implied by a more general statement about subvarieties of minimal cohomology class whose sum is a theta divisor.
متن کاملGeneric Vanishing and Minimal Cohomology Classes on Abelian Varieties
This paper is concerned with a relationship between the existence of subvarieties of principally polarized abelian varieties (ppav’s) having minimal cohomology class and the (generic) vanishing of certain sheaf cohomology, based on the Generic Vanishing criterion studied in [PP3]. This is in analogy with the well-known equivalence between a subvariety in projective space being of minimal degree...
متن کاملDerived Equivalence , Bgg Correspondence , and Cohomology
These notes are concerned with the behavior of various cohomology groups of the structure sheaf or the canonical bundle of a smooth projective variety, or of its Picard variety, under the action of Fourier-Mukai transforms and the BGG correspondence. They are prepared for lectures to be delivered at IHP Paris, and in Brasilia, in the summer of 2010. I thank the organizers of the respective even...
متن کاملذخیره 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 2008