Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

The Hodge- ${\mathcal D}$-conjecture for $\text{\rm K3}$ and Abelian surfaces


Authors: Xi Chen and James D. Lewis
Journal: J. Algebraic Geom. 14 (2005), 213-240
DOI: https://doi.org/10.1090/S1056-3911-04-00390-X
Published electronically: December 30, 2004
MathSciNet review: 2123228
Full-text PDF

Abstract | References | Additional Information

Abstract: Let $X$ be a projective algebraic manifold, and $\text{CH}^{k}(X,1)$ the higher Chow group, with corresponding real regulator $\text{r}_{k,1}\otimes {{\mathbb R}}: \text{CH}^k(X, 1)\otimes {{\mathbb R}} \to H_{\mathcal D}^{2k-1}(X,{{\mathbb R}}(k))$. If $X$ is a general K3 surface or Abelian surface, and $k=2$, we prove the Hodge- ${\mathcal D}$-conjecture, i.e. the surjectivity of $\text{r}_{2,1}\otimes {{\mathbb R}}$. Since the Hodge- ${\mathcal D}$-conjecture is not true for general surfaces in ${\mathbb P}^{3}$ of degree $\geq 5$, the results in this paper provide an effective bound for when this conjecture is true.


References [Enhancements On Off] (What's this?)


Additional Information

Xi Chen
Affiliation: 632 Central Academic Building, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Email: xichen@math.ualberta.ca

James D. Lewis
Affiliation: 632 Central Academic Building, University of Alberta, Edmonton, Alberta T6G 2G1, CANADA
Email: lewisjd@gpu.srv.ualberta.ca

DOI: https://doi.org/10.1090/S1056-3911-04-00390-X
Received by editor(s): April 11, 2003
Received by editor(s) in revised form: November 2, 2003
Published electronically: December 30, 2004
Additional Notes: Both authors were partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
Comments: jag-query@ams.org
AMS Website