English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We establish a connection between the theory of Ulrich sheaves and$\mathbb{A}^1$-homotopy theory. For instance, we prove that the$\mathbb{A}^1$-degree of a morphism between projective varieties, that isrelatively oriented by an Ulrich sheaf, is constant on the target even when itis not $\mathbb{A}^1$-connected. Further if an embedded projective variety isthe support of a symmetric Ulrich sheaf of rank one, the $\mathbb{A}^1$-degreeof all its linear projections can be read off in an explicit way from the freeresolution of the Ulrich sheaf. Finally, we construct an Ulrich sheaf on thesecant variety of a curve and use this to define an arithmetic version ofViro's encomplexed writhe for curves in $\mathbb{P}^3$. This can be consideredto be an arithmetic analogue of a link invariant.

Secant varieties of curves, Ulrich bundles and the arithmetic writhe