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5
Eisenbud-Goto conjecture predicted that the Castelnuovo-Mumford regularity
${\rm reg}(X)$ of a non-degenerate projective variety $X\subset \mathbb{P}^N$
is bounded by the $\deg(X)-{\rm codim}(X,\mathbb{P}^N)+1$, where $\deg(X)$ stands for the degree of $X$. This conjecture was stated by Eisenbud ...
In algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf F over projective space Pn is the smallest integer r such that it is r-regular, meaning that
H
i
(
P
n
,
F
(
r
−
i
)
)
=
0
{\displaystyle H^{i}(\mathbf {P} ^{n},F(r-i))=0\,}
whenever i > 0. The regularity of a subscheme is defined to be t...
I worked this theory : A new generalization of the dimension?
I have a theorem about dimensions which is more general and simple than for matroids.
Definition 1: A structure $S$, is a pair $(X, \mathcal T)$ with $X$ a set and $\mathcal T$ a set of subsets of $X$ which is stable w.r.t. arbit...
