Mathematics#18 in February 2026 EditionDerived categories of coherent sheaves on singular algebraic varieties and categorical resolution of singularities
Laurent Beaulieu, Anika Mehta, Christoph Schmidt et al.
OPENSTEM EDITORIAL SUMMARY
What the research examines
The authors construct smooth non-commutative categorical resolutions of singularities for quotient singularities and determinantal varieties, proving the existence of tilting bundles and semiorthogonal decompositions of their derived categories.
Why it may matter
Advances homological mirror symmetry, birational geometry, and non-commutative algebraic geometry.
What to examine carefully
Explicit tilting bundles are currently restricted to isolated quotient singularities with finite abelian stabilizers.
Editorial scope: This is a concise, independently written introduction based on the publisher information, not a full systematic review or independent replication. It must not replace reading the original methods, limitations and conclusions.
STUDENT RESEARCH LENS · ORIGINAL OPENSTEM NOTES
Try a small, reproducible follow-up
Compute Ext-groups between line bundles on singular projective curves to construct quiver representations of derived categories.
Questions to investigate
- How does the categorical resolution compare to classical crepant geometric blow-ups in the sense of McKay?
- What invariants are preserved across mutation of exceptional collections?
These are independently proposed educational investigations, not activities that the original research authors claim to have completed.
Publication & researcher information
JournalJournal of Algebraic Geometry
Published online2026-02-13
Authors (selected)Laurent Beaulieu, Anika Mehta, Christoph Schmidt et al.
University / laboratorySorbonne Université
CountryFrance
Multi-author research may involve universities in several countries. Unverified institutions and contact addresses are not inferred from authors' names.