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Investigate low-degree rational projections and determine the degree of irrationality for polarized varieties, focusing on general K3 and abelian surfaces.

August 20, 2026ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZEOpen Access

The polarized degree of irrationality of K3 surfaces

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Investigate low-degree rational projections and determine the degree of irrationality for polarized varieties, focusing on general K3 and abelian surfaces.
Constructed low-degree rational projections to projective spaces using kernel bundles associated with polarized varieties (X, L).
Analyzed families of minimal degree projections on very general K3 surfaces of genus 4, 5, and 6, and extended constructions to hyper-Kähler varieties.
Determined that the degree of irrationality equals 3 for both very general (1,6)-polarized abelian surfaces and very general genus 6 K3 surfaces.
Established new upper bounds on the degree of irrationality for K3 surfaces of arbitrary genus.
Constructed new generically finite rational maps of low degree connecting select hyper-Kähler and abelian varieties to projective spaces.

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Implication

Geometric analysis reveals low-degree rational projections for polarized K3 and abelian surfaces, establishing exact degrees of irrationality and new bounds across algebraic varieties.

Cite This Study

Federico Moretti (2026) studied this question.

synapsesocial.com/papers/6a86b4cb8a91293e6a1cc3e8 https://doi.org/10.2422/2036-2145.202506_015

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Implication

Geometric analysis reveals low-degree rational projections for polarized K3 and abelian surfaces, establishing exact degrees of irrationality and new bounds across algebraic varieties.

The polarized degree of irrationality of K3 surfaces

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Discussion

Implication

Cite This Study

The polarized degree of irrationality of K3 surfaces

Key Points

Discussion

Implication

Cite This Study

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