Work

Noncommutative Resolutions of Singularities

Year: 2025

Type: article

Abstract: Singularities in algebraic varieties present profound challenges in both classical and modern geometry. While Hironaka’s resolution of singularities provides a powerful tool in the commutative setting, many situations in higher-dimensional geometry and representation theory call for alternative approaches. This paper explores noncommutative resolutions—particularly noncommutative crepant resolutions (NCCRs)—as a means to “smooth out” singular spaces via noncommutative algebras. We review the theoretical foundations, provide key examples illustrating the construction of noncommutative resolutions, discuss their applications in fields such as string theory and representation theory, and outline open problems and future directions.

Source: International Journal of Scientific Research in Science Engineering and Technology

DOI: 10.32628/ijsrset25122101

Authors: Yashank Mittal, Dr. Narendra Swami

Institution: Shri Jagdishprasad Jhabarmal Tibrewala University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408182699

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