2,067 research outputs found
On the intersection of ACM curves in \PP^3
Bezout's theorem gives us the degree of intersection of two properly
intersecting projective varieties. As two curves in P^3 never intersect
properly, Bezout's theorem cannot be directly used to bound the number of
intersection points of such curves. In this work, we bound the maximum number
of intersection points of two integral ACM curves in P^3. The bound that we
give is in many cases optimal as a function of only the degrees and the initial
degrees of the curves
Ideals of general forms and the ubiquity of the Weak Lefschetz property
Let be positive integers and let be an
ideal generated by general forms of degrees , respectively, in a
polynomial ring with variables. When all the degrees are the same we
give a result that says, roughly, that they have as few first syzygies as
possible. In the general case, the Hilbert function of has been
conjectured by Fr\"oberg. In a previous work the authors showed that in many
situations the minimal free resolution of must have redundant terms which
are not forced by Koszul (first or higher) syzygies among the (and hence
could not be predicted from the Hilbert function), but the only examples came
when . Our second main set of results in this paper show that further
examples can be obtained when . We also show that if
Fr\"oberg's conjecture on the Hilbert function is true then any such redundant
terms in the minimal free resolution must occur in the top two possible degrees
of the free module. Related to the Fr\"oberg conjecture is the notion of Weak
Lefschetz property. We continue the description of the ubiquity of this
property. We show that any ideal of general forms in has
it. Then we show that for certain choices of degrees, any complete intersection
has it and any almost complete intersection has it. Finally, we show that most
of the time Artinian ``hypersurface sections'' of zeroschemes have it.Comment: 24 page
Cohomological characterization of vector bundles on multiprojective spaces
We show that Horrock's criterion for the splitting of vector bundles on
\PP^n can be extended to vector bundles on multiprojective spaces and to
smooth projective varieties with the weak CM property (see Definition 3.11). As
a main tool we use the theory of -blocks and Beilinson's type spectral
sequences. Cohomological characterizations of vector bundles are also showed
Stellar Metallicity Gradients in SDSS galaxies
We infer stellar metallicity and abundance ratio gradients for a sample of
red galaxies in the Sloan Digital Sky Survey (SDSS) Main galaxy sample. Because
this sample does not have multiple spectra at various radii in a single galaxy,
we measure these gradients statistically. We separate galaxies into stellar
mass bins, stack their spectra in redshift bins, and calculate the measured
absorption line indices in projected annuli by differencing spectra in
neighboring redshift bins. After determining the line indices, we use stellar
population modeling from the EZ\_Ages software to calculate ages,
metallicities, and abundance ratios within each annulus. Our data covers the
central regions of these galaxies, out to slightly higher than . We
find detectable gradients in metallicity and relatively shallow gradients in
abundance ratios, similar to results found for direct measurements of
individual galaxies. The gradients are only weakly dependent on stellar mass,
and this dependence is well-correlated with the change of with mass.
Based on this data, we report mean equivalent widths, metallicities, and
abundance ratios as a function of mass and velocity dispersion for SDSS
early-type galaxies, for fixed apertures of 2.5 kpc and of 0.5 .Comment: 19 pages; 8 tables, 12 figures. Submitted to ApJ for publicatio
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