Simple Complex Tori of Algebraic Dimension 0
Tatiana Bandman, Yuri G. Zarhin
TL;DR
This paper constructs an infinite family of simple complex tori with algebraic dimension zero and Picard number zero across all complex dimensions greater than one, using Galois theory.
Contribution
It provides an explicit construction of simple complex tori with specific algebraic properties in all dimensions greater than one.
Findings
Existence of infinite family of such tori in all dimensions >1
Construction method using Galois theory
Tori have algebraic dimension 0 and Picard number 0
Abstract
Using Galois theory, we construct explicitly (in all complex dimensions >1) an infinite family of simple complex tori of algebraic dimension 0 with Picard number 0.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Advanced Combinatorial Mathematics