Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Powers of Ideals and Fibers of Morphisms   Let X\subset PP^n be a projective scheme over a field, and let phi:X --> Y be
a finite morphism. Our main result is a formula in terms of global data for the
maximum of the Castelnuovo-Mumford regularity of the fibers of \phi, considered
as subschemes of \PP^n.
  From an algebraic point of view, our formula is related to the theorem of
Cutkosky-Herzog-Trung and Kodiyalam showing that for any homogeneous ideal I in
a standard graded algebra S, the regularity of I^t can be written as
dt+\epsilon for some non-negative integers d, \epsilon, and all large t. In the
special case where I contains a power of S_+ and is generated by forms of a
single degree, our formula gives an interpretation of \epsilon: it is one less
than the maximum regularity of a fiber of the morphism associated to I.
  These formulas have strong consequences for ideals generated by generic
forms.

36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th