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/

Zendy Plus

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

Zendy Tools

Zendy Open

In characteristic zero, the residual order constitutes, after the localmultiplicity, the second key invariant for the resolution of singularities. Itis defined as the order of the coefficient ideal in a local hypersurface ofmaximal contact, minus the exceptional multiplicities. It does not increaseunder blowup in permissible centers as long as the local multiplicity remainsconstant. In positive characteristic, however, the residual order (defined nowas the maximum over all smooth local hypersurfaces) may increase under blowup.In the article we analyze in detail the circumstances when this happens. Thismay help to develop a modification of the residual order which does work inpositive characteristic.

Characterizing the increase of the residual order under blowup in positive characteristic