Zusammenfassung
This paper stems from the observation (arising from work of Delzant) that "most" Kahler groups G virtually algebraically fiber, that is, admit a finite index subgroup that maps onto Z with finitely generated kernel. For the remaining ones, the Albanese dimension of all finite index subgroups is at most one, that is, they have virtual Albanese dimension va(G) <= 1. We show that the existence of ...
Zusammenfassung
This paper stems from the observation (arising from work of Delzant) that "most" Kahler groups G virtually algebraically fiber, that is, admit a finite index subgroup that maps onto Z with finitely generated kernel. For the remaining ones, the Albanese dimension of all finite index subgroups is at most one, that is, they have virtual Albanese dimension va(G) <= 1. We show that the existence of algebraic fibrations has implications in the study of coherence and higher BNSR invariants of the fundamental group of aspherical Kahler surfaces. The class of Kahler groups with va(G)=1 includes virtual surface groups. Further examples exist; nonetheless, they exhibit a strong relation with surface groups. In fact, we show that the Green-Lazarsfeld sets of groups with va(G)=1 (virtually) coincide with those of surface groups, and furthermore that the only virtually RFRS groups with va(G)=1 are virtually surface groups.
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