On the log canonical ring in Kodaira dimension two
Haidong Liu
TL;DR
This paper proves that for projective log canonical pairs with Kodaira dimension two, the associated log canonical ring is finitely generated, advancing understanding in algebraic geometry.
Contribution
It establishes the finite generation of the log canonical ring specifically for pairs with Kodaira dimension two, filling a gap in the minimal model program.
Findings
Log canonical ring is finitely generated for Kodaira dimension two.
Supports the minimal model program in algebraic geometry.
Advances classification theory of algebraic varieties.
Abstract
We prove that the log canonical ring of a projective log canonical pair in Kodaira dimension two is finitely generated.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models