Murre’s Conjectures and Explicit Chow–künneth Projectors for Varieties with a Nef Tangent Bundle
نویسندگان
چکیده
In this paper, we investigate Murre’s conjectures on the structure of rational Chow groups and exhibit explicit Chow–Künneth projectors for some examples. More precisely, the examples we study are the varieties which have a nef tangent bundle. For surfaces and threefolds which have a nef tangent bundle explicit Chow–Künneth projectors are obtained which satisfy Murre’s conjectures and the motivic Hard Lefschetz theorem is verified.
منابع مشابه
Murre’s Conjectures and Explicit Chow–künneth Projectors for Some Varieties
In this paper, we investigate Murre’s conjectures on the structure of rational Chow groups and exhibit explicit Chow–Künneth projectors for some examples. More precisely, the examples we study are the varieties which have a nef tangent bundle. For surfaces and threefolds which have a nef tangent bundle explicit Chow–Künneth projectors are obtained which satisfy Murre’s conjectures and the motiv...
متن کاملAbsolute Chow–künneth Decomposition for Rational Homogeneous Bundles and for Log Homogeneous Varieties
In this paper, we prove that rational homogeneous bundles and log homogeneous varieties (studied by M. Brion) have an absolute Chow–Künneth decomposition. This strengthens the earlier paper by us on small dimensional varieties with a NEF tangent bundle, and using Hwang-Mok’s results, we get the results for new cases in higher dimension as well, for instance upto dimension four.
متن کاملMurre’s Conjecture for a Rational Homogeneous Bundle over a Variety
In this paper, we investigate Murre’s conjectures on the structure of rational Chow groups for a rational homogeneous bundle Z → S over a smooth variety. Absolute Chow-Künneth projectors are exhibited for Z whenever S has a Chow–Künneth decomposition.
متن کاملOn Murre’s conjectures for blow-ups: a constructive approach
We show, by an explicit construction of the relevant Chow-Kunneth projectors, that if X is the quotient of a smooth projective variety by a finite group action and Y is obtained from X by blowing up a finite set of points, then (under appropriate hypotheses) each of Murre’s conjectures holds for Y if and only if it holds for X. The novelty of our approach is that, finite dimensionality of the c...
متن کاملChow–künneth Decomposition for Special Varieties
In this paper we investigate Murre’s conjecture on the Chow–Künneth decomposition for two classes of examples. We look at the universal families of smooth curves over spaces which dominate the moduli space Mg, in genus at most 8 and show existence of a Chow–Künneth decomposition. The second class of examples include the representation varieties of a finitely generated group with one relation. T...
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 2007