Generic vanishing and minimal cohomology classes on abelian varieties

Giuseppe Pareschi; Mihnea Popa

doi:10.1007/s00208-007-0146-7

Generic vanishing and minimal cohomology classes on abelian varieties

Giuseppe Pareschi, Mihnea Popa^*

^*Corresponding author for this work

Mathematics

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

19 Scopus citations

Abstract

We establish a-and conjecture further-relationship between the existence of subvarieties representing minimal cohomology classes on principally polarized abelian varieties, and the generic vanishing of the cohomology of twisted ideal sheaves. The main ingredient is the Generic Vanishing criterion established in Pareschi G. and Popa M. (GV-sheaves, Fourier-Mukai transform, and Generic Vanishing. Preprint math.AG/0608127), based on the Fourier-Mukai transform.

Original language	English (US)
Pages (from-to)	209-222
Number of pages	14
Journal	Mathematische Annalen
Volume	340
Issue number	1
DOIs	https://doi.org/10.1007/s00208-007-0146-7
State	Published - Jan 2008

Funding

MP was partially supported by the NSF grant DMS 0500985 and by an AMS Centennial Fellowship.

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00208-007-0146-7

Cite this

@article{52151274f4434c42808d0e2c25ba966f,

title = "Generic vanishing and minimal cohomology classes on abelian varieties",

abstract = "We establish a-and conjecture further-relationship between the existence of subvarieties representing minimal cohomology classes on principally polarized abelian varieties, and the generic vanishing of the cohomology of twisted ideal sheaves. The main ingredient is the Generic Vanishing criterion established in Pareschi G. and Popa M. (GV-sheaves, Fourier-Mukai transform, and Generic Vanishing. Preprint math.AG/0608127), based on the Fourier-Mukai transform.",

author = "Giuseppe Pareschi and Mihnea Popa",

note = "Funding Information: MP was partially supported by the NSF grant DMS 0500985 and by an AMS Centennial Fellowship.",

year = "2008",

month = jan,

doi = "10.1007/s00208-007-0146-7",

language = "English (US)",

volume = "340",

pages = "209--222",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Generic vanishing and minimal cohomology classes on abelian varieties

AU - Pareschi, Giuseppe

AU - Popa, Mihnea

N1 - Funding Information: MP was partially supported by the NSF grant DMS 0500985 and by an AMS Centennial Fellowship.

PY - 2008/1

Y1 - 2008/1

N2 - We establish a-and conjecture further-relationship between the existence of subvarieties representing minimal cohomology classes on principally polarized abelian varieties, and the generic vanishing of the cohomology of twisted ideal sheaves. The main ingredient is the Generic Vanishing criterion established in Pareschi G. and Popa M. (GV-sheaves, Fourier-Mukai transform, and Generic Vanishing. Preprint math.AG/0608127), based on the Fourier-Mukai transform.

AB - We establish a-and conjecture further-relationship between the existence of subvarieties representing minimal cohomology classes on principally polarized abelian varieties, and the generic vanishing of the cohomology of twisted ideal sheaves. The main ingredient is the Generic Vanishing criterion established in Pareschi G. and Popa M. (GV-sheaves, Fourier-Mukai transform, and Generic Vanishing. Preprint math.AG/0608127), based on the Fourier-Mukai transform.

UR - http://www.scopus.com/inward/record.url?scp=35448977224&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35448977224&partnerID=8YFLogxK

U2 - 10.1007/s00208-007-0146-7

DO - 10.1007/s00208-007-0146-7

M3 - Article

AN - SCOPUS:35448977224

SN - 0025-5831

VL - 340

SP - 209

EP - 222

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 1

ER -

Generic vanishing and minimal cohomology classes on abelian varieties

Abstract

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this