Miura’s conjecture on nontrivial Fourier–Mukai partners

For a general Calabi–Yau threefold $X$ in the Picard-rank- $1$ family of degree- $33$ threefolds in $G(2,6)$ constructed by Inoue–Ito–Miura, there exists a non-birational Calabi–Yau threefold $Y$ in the Picard-rank- $1$ family of arithmetically Gorenstein degree- $21$ threefolds in $\mathbb{P}^8$ constructed by Schenck–Stillman–Yuan such that $Y$ is a non-trivial Fourier–Mukai partner of $X$ , equivalently $D^b(X)\simeq D^b(Y)$ via a Fourier–Mukai equivalence.

References

Primary source

arXiv

Additional references

The Last Picard Rank 1 Double-Mirror Calabi-Yau Pair? — arXiv — Michał Kapustka, Marco Rampazzo, Prajwal Samal

Posted 2 weeks ago · edited 2 weeks ago

Progress summary

Refreshed 2 weeks ago

Claimed solved

A September 2026 preprint claims to establish the predicted partner and derived equivalence, but the broader mirror conjecture remains open.

Miura’s conjecture predicts a non-birational Fourier–Mukai partner and a related double-mirror Calabi–Yau threefold. No proposer or original date is identified in the retrieved material.

September 2026 claimed resolution

Michał Kapustka, Marco Rampazzo, and Prajwal Samal claim that the predicted geometric correspondence and derived equivalence are established. Their preprint presents the resulting pair as a candidate double-mirror example, while the broader common-mirror-family interpretation remains conjectural.

Current status (as of September 2026): The predicted partner and derived equivalence are claimed established in an unrefereed preprint, but the broader common-mirror-family and double-mirror conjectures remain open.

Sources

No solutions have been posted yet.