Compositionality conjecture for partial flag supervarieties

From papers

Let X=Flag(p1q1,,ptqt;  V)X = \operatorname{\mathbf{Flag}}(p_1|q_1, \dots, p_t|q_t;\;V) be a flag supervariety of type τ\tau, and let YY be the variety associated to XX by the construction in the paper. A compositionality conjecture for partial flag supervarieties. The variety YY is compositional, with defining parameters Δ\Delta_\bullet of the form

Δh=cihpi+dihqi,\Delta_h = \sum c^h_i p_i + d^h_i q_i,

where cih,dihZc^h_i,d^h_i \in \mathbf{Z} depend only on τ\tau and are independent of the pip_i and qiq_i. This is motivated by calculations in the 22-step case and by the extension result; the conjecture asserts that the rank conditions arising from arbitrary compositions completely determine the relevant compositional variety for all partial flag supervarieties.

Progress summary

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

Sources & referencesView supporting material

Primary source

Abhik Pal, “Cohomology of Flag Superschemes and Syzygies of Compositional Varieties”, arXiv:2606.14953 (2026).

Solutions 0

No solutions have been posted yet.