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math.AC2021
On the effective reduction of an ideal
Tomasz Rodak, Adam Różycki, Stanisław Spodzieja
It is well known that in the Noetherian local ring with infinite residue field the reduction of $\mm$-primary ideal may be given in the form of a sufficiently general linear combin…
math.AG2021
Effective Bertini theorem and formulas for multiplicity and the local Łojasiewicz exponent
Tomasz Rodak, Adam Różycki, Stanisław Spodzieja
The classical Bertini theorem on generic intersection of an algebraic set with hyperplanes states the following: \emph{Let X be a nonsingular closed subvariety of ,…