Semiorthogonal
adj ·Rare ·Advanced level
Definitions
- 1 Having the property that every subcategory is in the set of orthogonal subcategories of every higher order subcategory. not-comparable
"For del Pezzo surfaces of degree at least 5, we construct explicit semiorthogonal decompositions by subcategories of modules over semisimple algebras arising as endomorphism algebras of vector bundles and we show how to retrieve information about the index of the surface from Brauer classes and Chern classes associated to these vector bundles.."
- 2 Either columnwise orthogonal (having the property that M'M is an identity matrix) or rowwise orthogonal (having the property that MM' is an identity matrix). not-comparable
- 3 Orthogonal to the corresponding approximation space. not-comparable
Example
More examples"For del Pezzo surfaces of degree at least 5, we construct explicit semiorthogonal decompositions by subcategories of modules over semisimple algebras arising as endomorphism algebras of vector bundles and we show how to retrieve information about the index of the surface from Brauer classes and Chern classes associated to these vector bundles.."
Etymology
From semi- + orthogonal.
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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.