A motivic study of generalized Burniat surfaces

C. Peters

doi:10.1007/s12188-018-0198-5

A motivic study of generalized Burniat surfaces

C. Peters

Discrete Mathematics

Research output: Contribution to journal › Article › Academic › peer-review

221 Downloads (Pure)

Abstract

Generalized Burniat surfaces are surfaces of general type with p _g= q and Euler number e= 6 obtained by a variant of Inoue’s construction method for the classical Burniat surfaces. I prove a variant of the Bloch conjecture for these surfaces. The method applies also to the so-called Sicilian surfaces introduced by Bauer et al. in (J Math Sci Univ Tokyo 22(2–15):55–111, 2015. arXiv:1409.1285v2). This implies that the Chow motives of all of these surfaces are finite-dimensional in the sense of Kimura.

Original language	English
Pages (from-to)	377-387
Number of pages	11
Journal	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
Volume	88
Issue number	2
DOIs	https://doi.org/10.1007/s12188-018-0198-5
Publication status	Published - 1 Oct 2018

Keywords

math.AG
14C15, 14C25, 14C30
Algebraic cycles
Sicilian surfaces
Finite-dimensional motives
Burniat surfaces
Chow groups
Inoue surfaces

Access to Document

10.1007/s12188-018-0198-5

1710.02370v1Final author version , 160 KB
published versionFinal published version, 298 KB

Cite this

@article{2e888fe989fd47788b8fb6cff577f251,

title = "A motivic study of generalized Burniat surfaces",

abstract = "Generalized Burniat surfaces are surfaces of general type with p g= q and Euler number e= 6 obtained by a variant of Inoue{\textquoteright}s construction method for the classical Burniat surfaces. I prove a variant of the Bloch conjecture for these surfaces. The method applies also to the so-called Sicilian surfaces introduced by Bauer et al. in (J Math Sci Univ Tokyo 22(2–15):55–111, 2015. arXiv:1409.1285v2). This implies that the Chow motives of all of these surfaces are finite-dimensional in the sense of Kimura. ",

keywords = "math.AG, 14C15, 14C25, 14C30, Algebraic cycles, Sicilian surfaces, Finite-dimensional motives, Burniat surfaces, Chow groups, Inoue surfaces",

author = "C. Peters",

year = "2018",

month = oct,

day = "1",

doi = "10.1007/s12188-018-0198-5",

language = "English",

volume = "88",

pages = "377--387",

journal = "Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - A motivic study of generalized Burniat surfaces

AU - Peters, C.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Generalized Burniat surfaces are surfaces of general type with p g= q and Euler number e= 6 obtained by a variant of Inoue’s construction method for the classical Burniat surfaces. I prove a variant of the Bloch conjecture for these surfaces. The method applies also to the so-called Sicilian surfaces introduced by Bauer et al. in (J Math Sci Univ Tokyo 22(2–15):55–111, 2015. arXiv:1409.1285v2). This implies that the Chow motives of all of these surfaces are finite-dimensional in the sense of Kimura.

AB - Generalized Burniat surfaces are surfaces of general type with p g= q and Euler number e= 6 obtained by a variant of Inoue’s construction method for the classical Burniat surfaces. I prove a variant of the Bloch conjecture for these surfaces. The method applies also to the so-called Sicilian surfaces introduced by Bauer et al. in (J Math Sci Univ Tokyo 22(2–15):55–111, 2015. arXiv:1409.1285v2). This implies that the Chow motives of all of these surfaces are finite-dimensional in the sense of Kimura.

KW - math.AG

KW - 14C15, 14C25, 14C30

KW - Algebraic cycles

KW - Sicilian surfaces

KW - Finite-dimensional motives

KW - Burniat surfaces

KW - Chow groups

KW - Inoue surfaces

UR - https://www.scopus.com/pages/publications/85055974730

U2 - 10.1007/s12188-018-0198-5

DO - 10.1007/s12188-018-0198-5

M3 - Article

VL - 88

SP - 377

EP - 387

JO - Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

JF - Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

IS - 2

ER -

A motivic study of generalized Burniat surfaces

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this