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March 19, 2026Journal fรผr die reine und angewandte Mathematik (Crelles Journal)0 citations

Admissible Subcategories Supported on Curves in Smooth Projective Varieties

Admissible subcategories supported on curves

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Authors

DPDmitrii Pirozhkov

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Overview

This research demonstrates the relationship between admissible subcategories and rational curves, implying new insights into derived categories.

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.

Cite This Study

Dmitrii Pirozhkov (2026) studied this question.

synapsesocial.com/papers/69bb928c496e729e6297ff72https://doi.org/10.1515/crelle-2026-0019
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