A seminormal scheme is a scheme whose affine coordinate rings are seminormal. A ring 
is seminormal when, for 
with 
, there is a unique 
satisfying 
and 
. This property is local and implies that the scheme
is reduced (Stacks Project n.d.). For example, ![C[t^2,t^3]](/images/equations/SeminormalScheme/Inline7.svg)
is not seminormal, since 
and 
require 
, which does not belong to this ring. Seminormality is one
of the hypotheses on the underlying scheme of a semi-log
canonical pair.
Seminormal Scheme
See also
Algebraic Normalization, Scheme, Semi-Log Canonical PairExplore with Wolfram|Alpha
References
Stacks Project. "Absolute Weak Normalization and Seminormalization." Tag 0EUK. https://stacks.math.columbia.edu/tag/0EUK.Cite this as:
Weisstein, Eric W. "Seminormal Scheme." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SeminormalScheme.html