Admissible subcategories supported on curves

Key Points

• This study investigates admissible subcategories of coherent sheaves supported on curves within smooth projective varieties.
• Analyzed one-dimensional irreducible components of varieties Z within the context of smooth projective varieties.
• Explored intersections of irreducible components with the canonical class of the variety.
• Proved properties related to nef bundles and derived categories.
• Established that every one-dimensional irreducible component of Z is a rational curve.
• Demonstrated at least one irreducible component in Z intersects the canonical class negatively when dim Z = 1.
• Confirmed that if a surface has a nef and effective canonical bundle, its derived category is indecomposable.
• Showed that a configuration of curves with non-negative self-intersections cannot support an admissible subcategory.

Abstract