Potentially stably rational del Pezzo surfaces over nonclosed fields
Yuri Tschinkel, Kaiqi Yang
TL;DR
This paper classifies Galois actions on Picard lattices of low-degree del Pezzo surfaces to identify those with no cohomological obstructions to stable rationality over nonclosed fields.
Contribution
It provides a classification of Galois actions on Picard lattices that lead to potentially stably rational del Pezzo surfaces of degrees 1, 2, and 3.
Findings
Identifies Galois actions with no cohomological obstructions
Classifies minimal del Pezzo surfaces over nonclosed fields
Highlights conditions for stable rationality
Abstract
We classify Galois actions on Picard lattices of del Pezzo surfaces of degrees 1,2, and 3 giving rise to minimal surfaces with no cohomological obstructions to stable rationality.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Polynomial and algebraic computation