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dc.contributor.author
Arbesfeld, Noah
dc.contributor.author
Lim, Woonam
dc.contributor.author
Oprea, Dragos
dc.contributor.author
Pandharipande, Rahul
dc.date.accessioned
2021-03-02T08:28:26Z
dc.date.available
2021-03-02T03:55:51Z
dc.date.available
2021-03-02T08:28:26Z
dc.date.issued
2021-06
dc.identifier.other
10.1016/j.geomphys.2021.104154
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/472335
dc.description.abstract
We study virtual invariants of Quot schemes parametrizing quotients of dimension at most 1 of the trivial sheaf of rank N on nonsingular projective surfaces. We conjecture that the generating series of virtual K-theoretic invariants are given by rational functions. We prove rationality for several geometries including punctual quotients for all surfaces and dimension 1 quotients for surfaces X with pg>0. We also show that the generating series of virtual cobordism classes can be irrational. Given a K-theory class on X of rank r, we associate natural series of virtual Segre and Verlinde numbers. We show that the Segre and Verlinde series match in the following cases: • [(i)] Quot schemes of dimension 0 quotients, • [(ii)] Hilbert schemes of points and curves over surfaces with pg>0, • [(iii)] Quot schemes of minimal elliptic surfaces for quotients supported on fiber classes. Moreover, for punctual quotients of the trivial sheaf of rank N, we prove a new symmetry of the Segre/Verlinde series exchanging r and N. The Segre/Verlinde statements have analogues for punctual Quot schemes over curves. © 2021 Elsevier B.V.
en_US
dc.language.iso
en
en_US
dc.publisher
Elsevier
en_US
dc.subject
Hilbert and Quot schemes
en_US
dc.subject
K-theory
en_US
dc.subject
Segre and Verlinde series
en_US
dc.title
The virtual K-theory of Quot schemes of surfaces
en_US
dc.type
Journal Article
dc.date.published
2021-02-06
ethz.journal.title
Journal of Geometry and Physics
ethz.journal.volume
164
en_US
ethz.pages.start
104154
en_US
ethz.size
36 p.
en_US
ethz.grant
Cohomological field theories, algebraic cycles, and moduli spaces
en_US
ethz.grant
Moduli, algebraic cycles, and integration
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Amsterdam
en_US
ethz.publication.status
published
en_US
ethz.grant.agreementno
182181
ethz.grant.agreementno
786580
ethz.grant.fundername
SNF
ethz.grant.fundername
EC
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.funderDoi
10.13039/501100000780
ethz.grant.program
Projektförderung in Mathematik, Natur- und Ingenieurwissenschaften (Abteilung II)
ethz.grant.program
H2020
ethz.date.deposited
2021-03-02T03:56:14Z
ethz.source
SCOPUS
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2021-03-02T08:28:35Z
ethz.rosetta.lastUpdated
2021-03-02T08:28:35Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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