Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Expecting the unexpected: quantifying the persistence of unexpected
  hypersurfaces   If $X \subset \mathbb P^n$ is a reduced subscheme, we say that $X$ admits an
unexpected hypersurface of degree $t$ for multiplicity $m$ if the imposition of
having multiplicity $m$ at a general point $P$ fails to impose the expected
number of conditions on the linear system of hypersurfaces of degree $t$
containing $X$. Conditions which either guarantee the occurrence of unexpected
hypersurfaces, or which ensure that they cannot occur, are not well understand.
We introduce new methods for studying unexpectedness, such as the use of
generic initial ideals and partial elimination ideals to clarify when it can
and when it cannot occur. We also exhibit algebraic and geometric properties of
$X$ which in some cases guarantee and in other cases preclude $X$ having
certain kinds of unexpectedness. In addition, we formulate a new way of
quantifying unexpectedness (our AV sequence), which allows us detect the extent
to which unexpectedness persists as $t$ increases but $t-m$ remains constant.
Finally, we study to what extent we can detect unexpectedness from the Hilbert
function of $X$.

9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin