Finiteness conjecture for regional fundamental groups of dlt rationally connected pairs

At least 3 years old · documented by

Let XX be a rationally connected variety, and let (X,Δ)(X,\Delta) be a dlt pair. Write π1reg(X)\pi_1^{\rm reg}(X) for the regional fundamental group. Finiteness conjecture for regional fundamental groups. The group π1reg(X)\pi_1^{\rm reg}(X) is finite.

The conjecture is motivated by the contrast between Fano type and singular rationally connected varieties: rationally connected varieties can have infinite regional fundamental group in the singular setting, but the source expects finiteness for dlt pairs. It remains open.

References

Primary source

Joaquín Moraga, “Coregularity of Fano varieties”, arXiv:2206.10834 (2022).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.