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Questions tagged [castelnuovo-mumford-regularity]

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4 votes
1 answer
140 views

Castelnuovo-Mumford regularity for tensor products of vector bundles

I believe this should be a well known result, but I wasn’t able to prove or find a good reference for it. Let $E$ and $F$ be $n$-regular, respectively $m$-regular vector bundles in the sense of ...
User43029's user avatar
  • 596
2 votes
0 answers
117 views

$m$-regularity of sheaves

This is Lemma 1.4 on Green and Lazarsfeld's Some results on the syzygies of finite sets and algebraic curves. Let $X$ be a closed subscheme of $\mathbb{P}^r$. Suppose the ideal sheaf $\mathcal{I}$ of $...
Li Li's user avatar
  • 419
5 votes
0 answers
548 views

Eisenbud-Goto conjecture in Positive Characteristic

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,\...
Joaquín Moraga's user avatar
3 votes
1 answer
439 views

Castelnuovo-Mumford regularity in multigraded case

Let $R=\oplus_{n\geq 0}R_n$ be a standard Noetherian commuative graded ring over a local ring $(A,m)$ where $R_0=A.$ Put $R_+=\oplus_{n\geq 1}R_n.$ Let $M$ be a finitely generated $\mathbb Z$-graded $...
Cusp's user avatar
  • 1,703
20 votes
4 answers
4k views

What is interesting/useful about Castelnuovo-Mumford regularity?

What is interesting/useful about Castelnuovo-Mumford regularity?
David Zureick-Brown's user avatar