Log Crepant Birational Maps and Derived Categories
Yujiro Kawamata
TL;DR
This paper explores the relationship between log crepant birational maps and derived categories, extending existing conjectures to the logarithmic setting and providing proof in the toric case.
Contribution
It extends the conjecture linking derived equivalence and K-equivalence to the logarithmic case and proves it specifically for toric varieties.
Findings
Confirmed the conjecture for toric varieties.
Extended the theory to the logarithmic setting.
Provided a new framework for understanding derived categories in birational geometry.
Abstract
We extend the conjecture on the derived equivalence and K-equivalence to the logarithmic case and prove it in the toric case.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology