Hirzebruch-Riemann-Roch for global matrix factorizations

2021/06/01 by Bumsig Kim, Kim, Bumsig
Computer Science · Engineering · Mathematics · #18E30 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Matrix Theory and Algorithms #Primary 14A22 #Secondary 16E40 #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2106.00435

openalex publication_date 2021/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a Hirzebruch-Riemann-Roch type formula for global matrix factorizations. This is established by an explicit realization of the abstract Hirzebruch-Riemann-Roch type formula of Shklarov. We also show a Grothendieck-Riemann-Roch type theorem.

Citations

• Chern Character for Global Matrix Factorizations
• Atiyah class and Chern character for global matrix factorizations
• A chain-level HKR-type map and a Chern character formula

Related

• Riemann-Roch for stacky matrix factorizations
• Canonical pairing and Hirzebruch-Riemann-Roch formula for matrix factorizations
• Atiyah class and Chern character for global matrix factorizations
• Riemann-Roch and Riemann-Hurwitz theorems for global fields
• Hirzebruch-Riemann-Roch and Lefschetz type formulas for finite dimensional algebras