Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upgraded methods for the effective computation of marked schemes on a
  strongly stable ideal   Let $J\subset S=K[x_0,...,x_n]$ be a monomial strongly stable ideal. The
collection $\Mf(J)$ of the homogeneous polynomial ideals $I$, such that the
monomials outside $J$ form a $K$-vector basis of $S/I$, is called a {\em
$J$-marked family}. It can be endowed with a structure of affine scheme, called
a {\em $J$-marked scheme}. For special ideals $J$, $J$-marked schemes provide
an open cover of the Hilbert scheme $\hilbp$, where $p(t)$ is the Hilbert
polynomial of $S/J$. Those ideals more suitable to this aim are the
$m$-truncation ideals $\underline{J}_{\geq m}$ generated by the monomials of
degree $\geq m$ in a saturated strongly stable monomial ideal $\underline{J}$.
Exploiting a characterization of the ideals in $\Mf(\underline{J}_{\geq m})$ in
terms of a Buchberger-like criterion, we compute the equations defining the
$\underline{J}_{\geq m}$-marked scheme by a new reduction relation, called {\em
superminimal reduction}, and obtain an embedding of $\Mf(\underline{J}_{\geq
m})$ in an affine space of low dimension. In this setting, explicit
computations are achievable in many non-trivial cases. Moreover, for every $m$,
we give a closed embedding $\phi_m: \Mf(\underline{J}_{\geq m})\hookrightarrow
\Mf(\underline{J}_{\geq m+1})$, characterize those $\phi_m$ that are
isomorphisms in terms of the monomial basis of $\underline{J}$, especially we
characterize the minimum integer $m_0$ such that $\phi_m$ is an isomorphism for
every $m\geq m_0$.

7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas