Simple connectedness conjecture for semi log canonical Fano varieties

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Let (X,Δ)(X, \Delta) be a projective semi log canonical pair, meaning a projective pair with semi log canonical singularities, such that −(KX+Δ)-(K_X+\Delta) is ample; equivalently, (X,Δ)(X, \Delta) is a semi log canonical Fano variety. Simple connectedness conjecture. Then XX is simply connected. This is presented as a special case of the conjecture for projective quasi-log canonical pairs. The preceding result establishes triviality of the algebraic fundamental group in the broader quasi-log canonical Fano setting, while triviality of the topological fundamental group remains the conjectural assertion.

References

Primary source

Osamu Fujino, “Pull-back of quasi-log structures”, arXiv:1401.1854 (2016).

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