Bloch’s conjecture for Catanese and Barlow surfaces
نویسنده
چکیده
Catanese surfaces are regular surfaces of general type with pg = 0. They specialize to double covers of Barlow surfaces. We prove that the CH0 group of a Catanese surface is equal to Z, which implies the same result for the Barlow surfaces.
منابع مشابه
Some Surfaces of General Type for Which Bloch’s Conjecture Holds
We give many examples of surfaces of general type with pg = 0 for which Bloch’s conjecture holds, for all values of K2 6= 9. Our surfaces are equipped with an involution. Let S be a smooth complex projective surface with pg(S) = 0. Bloch’s conjecture states that the Albanese map A0(S)0 → Alb(S) is an isomorphism, where A0(S)0 is the Chow group of 0-cycles of degree 0 on S. It is known for all s...
متن کاملOn the Scalar Curvature of Einstein Manifolds
We show that there are high-dimensional smooth compact manifolds which admit pairs of Einstein metrics for which the scalar curvatures have opposite signs. These are counter-examples to a conjecture considered by Besse [6, p. 19]. The proof hinges on showing that the Barlow surface has small deformations with ample canonical line bundle.
متن کامل2 00 1 Surfaces with p g = q = 2 and an irrational pencil
We classify all the irrational pencils over the surfaces of general type with pg = q = 2; as a byproduct it gives an evidence for the Catanese conjecture on surfaces of general type with pg = q = 2.
متن کاملSymplectic Involutions of K 3 Surfaces Act Trivially on CH 0 Claire Voisin
A symplectic involution on a K3 surface is an involution which preserves the holomorphic 2-form. We prove that such a symplectic involution acts as the identity on the CH0 group of the K3 surface, as predicted by Bloch’s conjecture. 2010 Mathematics Subject Classification: 14C25, 14J28
متن کاملTHE TATE CONJECTURE FOR A FAMILY OF SURFACES OF GENERAL TYPE WITH pg
We prove a big monodromy result for a smooth family of complex algebraic surfaces of general type, with invariants pg = q = 1 and K 2 = 3, that has been introduced by Catanese and Ciliberto. This is accomplished via a careful study of degenerations. As corollaries, when a surface in this family is defined over a finitely generated extension of Q, we verify the semisimplicity and Tate conjecture...
متن کامل