VIRTUAL ALGEBRAIC FIBRATIONS OF KÄHLER GROUPS

Author:

FRIEDL STEFAN,VIDUSSI STEFANO

Abstract

This paper stems from the observation (arising from work of Delzant) that “most” Kähler groups $G$ virtually algebraically fiber, that is, admit a finite index subgroup that maps onto $\mathbb{Z}$ 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 $va(G)\leqslant 1$. 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 Kähler surfaces. The class of Kähler 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

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3. Congruence RFRS towers;Annales de l'Institut Fourier;2022-09-12

4. BNS INVARIANTS AND ALGEBRAIC FIBRATIONS OF GROUP EXTENSIONS;Journal of the Institute of Mathematics of Jussieu;2021-09-21

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