On 3-canonical maps of varieties of Albanese fiber dimension one
Yuesen Chen
TL;DR
This paper investigates the properties of the 3-canonical map for varieties with Albanese fiber dimension one, demonstrating that it is generically birational under certain conditions related to the fiber genus.
Contribution
It proves the generic birationality of the 3-canonical map for varieties of Albanese fiber dimension one with fibers of genus 2, based on regularity of canonical sheaves.
Findings
3-canonical map is generically birational for certain varieties
Regularity of direct image of canonical sheaves is key
Genus of fibers influences the birationality
Abstract
In the present paper, we study the (twisted) 3-canonical map of varieties of Albanese fiber dimension one. Based on a theorem about the regularity of direct image of canonical sheaves, we prove that the 3-canonical map is generically birational when the genus of a general fiber of the Albanese map is 2.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds