Derived equivalence and birationality
Yu-Han Liu
TL;DR
This paper presents new proofs linking derived equivalence to birationality, establishing isomorphism of derived equivalent smooth projective curves and reaffirming birationality for varieties of general type.
Contribution
It provides alternative proofs for known results, strengthening the connection between derived equivalence and birational geometry.
Findings
Derived equivalent smooth projective curves are isomorphic.
Derived equivalence implies birationality for varieties of general type.
New proofs offer different perspectives on established theorems.
Abstract
A different proof to a known criterion of derived equivalence implying birationality is given. Derived equivalent smooth projective curves over an algebraically closed field are proved to be isomorphic. A different proof of derived equivalence implying birationality for varieties of general type (originally due to Kawamata) is given.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Polynomial and algebraic computation