Halphen pencils on quartic threefolds
Ivan Cheltsov, Ilya Karzhemanov
TL;DR
This paper classifies specific pencils on smooth quartic threefolds where the general element is a surface birational to a smooth surface of Kodaira dimension zero, advancing understanding of their geometric structure.
Contribution
It provides a complete classification of Halphen pencils on smooth quartic threefolds, identifying all such pencils with irreducible surfaces of Kodaira dimension zero.
Findings
Complete classification of Halphen pencils on quartic threefolds
Identification of conditions for surfaces of Kodaira dimension zero
New insights into the birational geometry of quartic threefolds
Abstract
For every smooth quartic threefold, we classify all pencils on it whose general element is an irreducible surface birational to a smooth surface of Kodaira dimension zero.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry