STABLE MAPS OF CURVES AND ALGEBRAIC EQUIVALENCE OF 1-CYCLES

János Kollár; Zhiyu Tian

doi:10.1215/00127094-2024-0045

STABLE MAPS OF CURVES AND ALGEBRAIC EQUIVALENCE OF 1-CYCLES

János Kollár
, Zhiyu Tian

Mathematics

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

Abstract

We show that algebraic equivalence of images of stable maps of curves lifts to deformation equivalence of the stable maps. The main applications concern A₁.X/, the group of 1-cycles modulo algebraic equivalence, for smooth, separably rationally connected varieties. If K=k is an algebraic extension, then the kernel of A₁.X_k/ ! A₁.X_K/ is at most Z=2Z. If k is finite, then the image equals the subgroup of Galois invariant cycles.

Original language	English (US)
Pages (from-to)	911-947
Number of pages	37
Journal	Duke Mathematical Journal
Volume	174
Issue number	5
DOIs	https://doi.org/10.1215/00127094-2024-0045
State	Published - Apr 1 2025

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1215/00127094-2024-0045

Cite this

@article{3202b1a0b9f74c7f91114764fd1a3856,

title = "STABLE MAPS OF CURVES AND ALGEBRAIC EQUIVALENCE OF 1-CYCLES",

abstract = "We show that algebraic equivalence of images of stable maps of curves lifts to deformation equivalence of the stable maps. The main applications concern A1.X/, the group of 1-cycles modulo algebraic equivalence, for smooth, separably rationally connected varieties. If K=k is an algebraic extension, then the kernel of A1.Xk/ ! A1.XK/ is at most Z=2Z. If k is finite, then the image equals the subgroup of Galois invariant cycles.",

author = "J{\'a}nos Koll{\'a}r and Zhiyu Tian",

year = "2025",

month = apr,

day = "1",

doi = "10.1215/00127094-2024-0045",

language = "English (US)",

volume = "174",

pages = "911--947",

journal = "Duke Mathematical Journal",

issn = "0012-7094",

publisher = "Duke University Press",

number = "5",

}

TY - JOUR

T1 - STABLE MAPS OF CURVES AND ALGEBRAIC EQUIVALENCE OF 1-CYCLES

AU - Kollár, János

AU - Tian, Zhiyu

PY - 2025/4/1

Y1 - 2025/4/1

N2 - We show that algebraic equivalence of images of stable maps of curves lifts to deformation equivalence of the stable maps. The main applications concern A1.X/, the group of 1-cycles modulo algebraic equivalence, for smooth, separably rationally connected varieties. If K=k is an algebraic extension, then the kernel of A1.Xk/ ! A1.XK/ is at most Z=2Z. If k is finite, then the image equals the subgroup of Galois invariant cycles.

AB - We show that algebraic equivalence of images of stable maps of curves lifts to deformation equivalence of the stable maps. The main applications concern A1.X/, the group of 1-cycles modulo algebraic equivalence, for smooth, separably rationally connected varieties. If K=k is an algebraic extension, then the kernel of A1.Xk/ ! A1.XK/ is at most Z=2Z. If k is finite, then the image equals the subgroup of Galois invariant cycles.

UR - https://www.scopus.com/pages/publications/105005499115

UR - https://www.scopus.com/pages/publications/105005499115#tab=citedBy

U2 - 10.1215/00127094-2024-0045

DO - 10.1215/00127094-2024-0045

M3 - Article

AN - SCOPUS:105005499115

SN - 0012-7094

VL - 174

SP - 911

EP - 947

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 5

ER -

STABLE MAPS OF CURVES AND ALGEBRAIC EQUIVALENCE OF 1-CYCLES

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this