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

Let X\subset PP^n be a projective scheme over a field, and let phi:X --> Y bea finite morphism. Our main result is a formula in terms of global data for themaximum of the Castelnuovo-Mumford regularity of the fibers of \phi, consideredas subschemes of \PP^n.  From an algebraic point of view, our formula is related to the theorem ofCutkosky-Herzog-Trung and Kodiyalam showing that for any homogeneous ideal I ina standard graded algebra S, the regularity of I^t can be written asdt+\epsilon for some non-negative integers d, \epsilon, and all large t. In thespecial case where I contains a power of S_+ and is generated by forms of asingle degree, our formula gives an interpretation of \epsilon: it is one lessthan the maximum regularity of a fiber of the morphism associated to I.  These formulas have strong consequences for ideals generated by genericforms.

Powers of Ideals and Fibers of Morphisms