On Examples of Supersingular and Rationally Chain Connected Threefolds
Santai Qu
TL;DR
This paper explores the relationship between supersingularity and rational-chain-connectivity in certain threefolds over fields of positive characteristic, establishing equivalences and providing examples of their coexistence.
Contribution
It demonstrates that for a specific class of threefolds, supersingularity and rational-chain-connectivity are equivalent, extending known results from K3 surfaces to threefolds.
Findings
Supersingularity and rational-chain-connectivity are equivalent for certain threefolds.
Examples exist of threefolds that are both supersingular and rationally chain connected.
The results generalize known properties from K3 surfaces to higher-dimensional varieties.
Abstract
In this work, we show that for a certain class of threefolds in positive characteristics, rational-chain-connectivity is equivalent to supersingularity. The same result is known for K3 surfaces with elliptic fibrations. And there are examples of threefolds that are both supersingular and rationally chain connected.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry