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dc.contributor.author
Pandharipande, Rahul
dc.contributor.author
Schmitt, Johannes
dc.date.accessioned
2021-02-24T14:30:58Z
dc.date.available
2021-02-05T03:57:28Z
dc.date.available
2021-02-24T14:30:58Z
dc.date.issued
2020
dc.identifier.issn
2491-6765
dc.identifier.other
10.46298/epiga.2020.volume4.5601
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/467825
dc.identifier.doi
10.3929/ethz-b-000467825
dc.description.abstract
While the Chow groups of 0-dimensional cycles on the moduli spaces of Deligne-Mumford stable pointed curves can be very complicated, the span of the 0-dimensional tautological cycles is always of rank 1. The question of whether a given moduli point [C,p_1,...,p_n] determines a tautological 0-cycle is subtle. Our main results address the question for curves on rational and K3 surfaces. If C is a nonsingular curve on a nonsingular rational surface of positive degree with respect to the anticanonical class, we prove [C,p_1,...,p_n] is tautological if the number of markings does not exceed the virtual dimension in Gromov-Witten theory of the moduli space of stable maps. If C is a nonsingular curve on a K3 surface, we prove [C,p_1,...,p_n] is tautological if the number of markings does not exceed the genus of C and every marking is a Beauville-Voisin point. The latter result provides a connection between the rank 1 tautological 0-cycles on the moduli of curves and the rank 1 tautological 0-cycles on K3 surfaces. Several further results related to tautological 0-cycles on the moduli spaces of curves are proven. Many open questions concerning the moduli points of curves on other surfaces (Abelian, Enriques, general type) are discussed.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Center for Direct Scientific Communication
en_US
dc.rights.uri
http://creativecommons.org/licenses/by-sa/4.0/
dc.subject
Chow groups
en_US
dc.subject
Moduli spaces of curves
en_US
dc.subject
Tautological rings
en_US
dc.title
Zero cycles on the moduli space of curves
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution-ShareAlike 4.0 International
dc.date.published
2020-09-03
ethz.journal.title
Épijournal de Géométrie Algébrique
ethz.journal.volume
4
en_US
ethz.pages.start
12
en_US
ethz.size
26 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.grant
Cohomological field theories, algebraic cycles, and moduli spaces
en_US
ethz.grant
Cohomology of moduli spaces
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Grenoble
en_US
ethz.publication.status
published
en_US
ethz.grant.agreementno
182181
ethz.grant.agreementno
162928
ethz.grant.fundername
SNF
ethz.grant.fundername
SNF
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
Projektförderung in Mathematik, Natur- und Ingenieurwissenschaften (Abteilung II)
ethz.grant.program
Projektförderung in Mathematik, Natur- und Ingenieurwissenschaften (Abteilung II)
ethz.date.deposited
2021-02-05T03:57:42Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2021-02-24T14:31:20Z
ethz.rosetta.lastUpdated
2021-02-24T14:31:20Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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