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Complex hypersurfaces in direct products of Riemann surfaces

Llosa Isenrich, Claudio 1
1 Institut für Algebra und Geometrie (IAG), Karlsruher Institut für Technologie (KIT)

Abstract:

We study smooth complex hypersurfaces in direct products of closed hyperbolic Riemann surfaces and give a classification in terms of their fundamental groups. This answers a question of Delzant and Gromov on subvarieties of products of Riemann surfaces in the smooth codimension one case. We also answer Delzant and Gromov’s question of which subgroups of a direct product of surface groups are Kähler for two classes: subgroups of direct products of three surface groups, and subgroups arising as the kernel of a homomorphism from the product of surface groups to Z$^3$. These results will be a consequence of answering the more general question of which subgroups of a direct product of surface groups are the image of a homomorphism from a Kähler group, which is induced by a holomorphic map, for the same two classes. This provides new constraints on Kähler groups.


Verlagsausgabe §
DOI: 10.5445/IR/1000172943
Veröffentlicht am 29.07.2024
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Zeitschriftenaufsatz
Publikationsdatum 28.06.2024
Sprache Englisch
Identifikator ISSN: 1472-2739, 1472-2747
KITopen-ID: 1000172943
Erschienen in Algebraic & Geometric Topology
Verlag Mathematical Sciences Publishers (MSP)
Band 24
Heft 3
Seiten 1467–1486
Nachgewiesen in Dimensions
Web of Science
Scopus
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