Relationships and universality of shifted logarithmic symplectic structures

Determine the relationships among shifted symplectic structures, twisted symplectic structures, and shifted log symplectic structures; construct a log compactification carrying a shifted log symplectic structure from a given shifted symplectic derived stack; and establish whether shifted log symplectic structures are universal among twisted symplectic structures.

Background

The paper develops shifted log symplectic structures as a specialization of twisted symplectic structures over the base stack A = [A1/G_m]. It proves a logarithmic Lagrangian intersection theorem showing that the derived log critical locus of a shifted log function carries a shifted log symplectic structure.

The authors explicitly leave unresolved the conceptual relationship between these three types of shifted structures, the converse problem of compactifying a shifted symplectic derived stack while preserving an appropriate logarithmic symplectic structure, and the possible universality of shifted log symplectic structures within twisted symplectic geometry.

References

We conclude this subsection by proposing a series of questions. What are the relationships among shifted symplectic structures , twisted symplectic structures , and shifted log symplectic structures? For example, the open complement of the virtual Cartier divisor of a $(-n)$-shifted log symplectic derived log stack is a $(-n)$-shifted symplectic derived stack. Conversely, given a shifted symplectic derived stack, can one construct a log compactification that carries a shifted log symplectic structure? Given that shifted log symplectic structures are special cases of twisted symplectic structures and the base stack for shifted log structures is $A:= [A1 / G_m]$, are shifted log symplectic structures in some sense universal among twisted symplectic structures?

— Deligne--Faltings Logarithmic Derived Geometry with a View towards Logarithmic GLSM  (2610.23803 - Janda et al., 16 Oct 2026) in Section 2, subsection “Shifted Logarithmic Symplectic Structures,” concluding paragraph