Incomplete Fourier–Mukai Limit-Cycle Extraction

Definitions and mathematical statement

The supplied record asks: given the degeneration and Fourier--Mukai transform referred to in the source report, determine the limit cycle $\phi_0$ of $\phi_\eta$.

Here $\phi_\eta$ and $\phi_0$ are retained as source notation only. The record does not define the degeneration, its base or fibers, the Fourier--Mukai transform, either cycle, or the operation by which a limit cycle is obtained. In particular, the meaning of the index $\eta$, the ambient spaces, the type of cycles, and any equivalence relation on cycles are unspecified. Thus no precise limit or specialization formula can be stated from the supplied evidence.

The supplied statement status is unrecoverable, and no clean statement is supplied. The question above preserves the extracted target but is not a complete mathematical formulation. Definitions, hypotheses, domains, boundary conditions, and quantifiers must be recovered from the source before a precise problem can be stated.

Short English statement

The extracted question asks for a limit cycle $\phi_0$ associated with $\phi_\eta$, a degeneration, and a Fourier--Mukai transform. None of these objects or the limiting operation is defined in the supplied record, so the intended mathematical problem remains unrecoverable. Its open label is supplied curation, not an independently verified mathematical conclusion.

Sources

• Local registry: data/unsolvedmath/problems.json, permanent UnsolvedMath ID $30001354$, source problem code catalogue entry, title "Incomplete Fourier--Mukai Limit-Cycle Extraction," in the Oberwolfach Reports Open Problems collection. The record preserves the original extraction for provenance and supplies no clean statement.
• Supplied report citation: Complex Algebraic Geometry (2010), Oberwolfach Reports, DOI 10.4171/owr/2009/44, pp. 2483--2544. Source URL and supplied literature reference labeled "original OWR report": https://doi.org/10.4171/owr/2009/44. The collection describes these reports as documenting mathematical workshops and their open-problem discussions. The report has not been independently consulted for this draft.
• Attribution: no proposer is supplied. The registry gives proposed year $2009$; the supplied citation labels the report $2010$, while the DOI and year tag contain $2009$. These source details are retained without resolving their relationship.
• Supplied literature assessment, checked 2026-08-21: status open. The assessment says that the extracted question concerns the limit of an unspecified quantity $\phi$ in an incomplete passage, and that no mathematical definition or theorem identifies a resolved claim. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment. Its status and cited claims require independent verification.