149 research outputs found
A combinatorial description of finite O-sequences and aCM genera
The goal of this paper is to explicitly detect all the arithmetic genera of
arithmetically Cohen-Macaulay projective curves with a given degree . It is
well-known that the arithmetic genus of a curve can be easily deduced
from the -vector of the curve; in the case where is arithmetically
Cohen-Macaulay of degree , must belong to the range of integers
. We develop an algorithmic procedure that
allows one to avoid constructing most of the possible -vectors of . The
essential tools are a combinatorial description of the finite O-sequences of
multiplicity , and a sort of continuity result regarding the generation of
the genera. The efficiency of our method is supported by computational
evidence. As a consequence, we single out the minimal possible
Castelnuovo-Mumford regularity of a curve with Cohen-Macaulay postulation and
given degree and genus.Comment: Final versio
Upgraded methods for the effective computation of marked schemes on a strongly stable ideal
Let be a monomial strongly stable ideal. The
collection \Mf(J) of the homogeneous polynomial ideals , such that the
monomials outside form a -vector basis of , is called a {\em
-marked family}. It can be endowed with a structure of affine scheme, called
a {\em -marked scheme}. For special ideals , -marked schemes provide
an open cover of the Hilbert scheme \hilbp, where is the Hilbert
polynomial of . Those ideals more suitable to this aim are the
-truncation ideals generated by the monomials of
degree in a saturated strongly stable monomial ideal .
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
-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 ,
we give a closed embedding \phi_m: \Mf(\underline{J}_{\geq m})\hookrightarrow
\Mf(\underline{J}_{\geq m+1}), characterize those that are
isomorphisms in terms of the monomial basis of , especially we
characterize the minimum integer such that is an isomorphism for
every .Comment: 28 pages; this paper contains and extends the second part of the
paper posed at arXiv:0909.2184v2[math.AG]; sections are now reorganized and
the general presentation of the paper is improved. Final version accepted for
publicatio
Segments and Hilbert schemes of points
Using results obtained from the study of homogeneous ideals sharing the same
initial ideal with respect to some term order, we prove the singularity of the
point corresponding to a segment ideal with respect to the revlex term order in
the Hilbert scheme of points in . In this context, we look inside
properties of several types of "segment" ideals that we define and compare.
This study led us to focus our attention also to connections between the shape
of generators of Borel ideals and the related Hilbert polynomial, providing an
algorithm for computing all saturated Borel ideals with the given Hilbert
polynomial.Comment: 19 pages, 2 figures. Comments and suggestions are welcome
Minimal Castelnuovo-Mumford regularity for a given Hilbert polynomial
Let be an algebraically closed field of null characteristic and a
Hilbert polynomial. We look for the minimal Castelnuovo-Mumford regularity
of closed subschemes of projective spaces over with Hilbert
polynomial . Experimental evidences led us to consider the idea that
could be achieved by schemes having a suitable minimal Hilbert
function. We give a constructive proof of this fact. Moreover, we are able to
compute the minimal Castelnuovo-Mumford regularity of
schemes with Hilbert polynomial and given regularity of the
Hilbert function, and also the minimal Castelnuovo-Mumford regularity of
schemes with Hilbert function . These results find applications in the study
of Hilbert schemes. They are obtained by means of minimal Hilbert functions and
of two new constructive methods which are based on the notion of
growth-height-lexicographic Borel set and called ideal graft and extended
lifting.Comment: 21 pages. Comments are welcome. More concise version with a slight
change in the title. A further revised version has been accepted for
publication in Experimental Mathematic
Projections of climate extremes under potential climate change as represented by changing equator to pole temperature gradient and land ocean temperature contrast.
Under climate variability and anthropogenic forcing, the Equator-to-Pole Temperature Gradient
(EPG) and the Ocean-Land Temperature Contrast (OLC) undergo systematic changes, which can be
associated with the equatorial pacific circulation patterns via teleconnections, and with the Atlantic
Meridional Overturning Circulation (AMOC) via ocean-atmosphere coupling.
We couple the Lorenz ’84 atmospheric model, a Box AMOC model (after Roebber 1994), and an
ENSO coupled ocean-atmosphere model (Tziperman et al, 1994) to explore the sensitivity of the
strength, position and other statistics of the mid-latitude wind components to changes in the
aforementioned systems and components. Sea ice and water balances are not explicitly modeled.
We then develop and discuss projections of the changes in persistence, low frequency variability,
and frequency of extremes in key climatic parameters, as specific climate changes, anticipated under
anthropogenic forcing in the 21st century, are postulated
Effect of somatosensory amplification and trait anxiety on experimentally induced orthodontic pain
The perception of pain varies considerably across individuals and is affected by psychological traits. This study aimed to investigate the combined effects of somatosensory amplification and trait anxiety on orthodontic pain. Five-hundred and five adults completed the State Trait Anxiety Inventory (STAI) and the Somatosensory Amplification Scale (SSAS). Individuals with combined STAI and SSAS scores below the 20th percentile (LASA group: five men and 12 women; mean age ± SD = 22.4 ± 1.3 yr) or above the 80th percentile (HASA group: 13 men and seven women; mean age ± SD = 23.7 ± 1.0 yr) were selected and filled in the Oral Behaviors Checklist (OBC). Orthodontic separators were placed for 5 d in order to induce experimental pain. Visual analog scales (VAS) were administered to collect ratings for occlusal discomfort, pain, and perceived stress. Pressure pain thresholds (PPT) were measured. A mixed regression model was used to evaluate pain and discomfort ratings over the 5-d duration of the study. At baseline, the LASA group had statistically significantly higher PPT values for the masseter muscle than did the HASA group. During the experimental procedure, the HASA group had statistically significantly higher discomfort and pain. A significant difference in pain ratings during the 5 d of the study was found for subjects in the HASA group. Higher OBC values were statistically significantly positively associated with pain. Somatosensory amplification and trait anxiety substantially affect experimentally induced orthodontic pain
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