Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Results on Asymptotic Regularity of Ideal Sheaves   Let $\mathscr{I}$ be an ideal sheaf on $P^n$ defining a subscheme $X$.
Associated to $\mathscr{I}$ there are two elementary invariants: the invariant
$s$ which measures the positivity of $\mathscr{I}$, and the minimal number $d$
such that $\mathscr{I}(d)$ is generated by its global sections. It is now clear
that the asymptotic behavior of $\reg \mathscr{I}^t$ is governed by $s$ but
usually not linear. In this paper, we first describe the linear behavior of the
asymptotic regularity by showing that if $s=d$, i.e., $s$ reaches its maximal
value, then for $t$ large enough $\reg \mathscr{I}^t=dt+e$ for some positive
constant $e$. We then turn to concrete geometric settings to study the
asymptotic regularity of $\mathscr{I}$ in the case that $X$ is a nonsingular
variety embedded by a very ample adjoint line bundle. Our approach also gives
regularity bounds for $\mathscr{I}^t$ once we know $\reg \mathscr{I}$ and
assume that $X$ is a local complete intersection.

29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci