1,330 research outputs found
Generic Syzygy Schemes
For a finite dimensional vector space G we define the k-th generic syzygy
scheme Gensyz_k(G) by explicit equations. We show that the syzygy scheme Syz(f)
of any syzygy in the linear strand of a projective variety X which is cut out
by quadrics is a cone over a linear section of a corresponding generic syzygy
scheme. We also give a geometric description of Gensyz_k(G) for k=0,1,2. In
particular Gensyz_2(G) is the union of a Pl"ucker embedded Grassmannian and a
linear space. From this we deduce that every smooth, non-degenerate projective
curve C which is cut out by quadrics and has a p-th linear syzygy of rank p+3
admits a rank 2 vector bundle E with det E = O_C(1) and h^0(E) at least p+4.Comment: 12 Pages. This paper is a completely rewritten version of the first
part of math.AG/0108078. It also contains several new result
Solar-wind predictions for the Parker Solar Probe orbit
The scope of this study is to model the solar-wind environment for the Parker
Solar Probe's unprecedented distances down to 9.86 Rs in its mission phase
during 2018-2025. The study is performed within the CGAUSS project which is the
German contribution to the PSP mission as part of the WISPR imager on PSP. We
present an empirical solar-wind model for the inner heliosphere which is
derived from OMNI and Helios data. The sunspot number (SSN) and its predictions
are used to derive dependencies of solar-wind parameters on solar activity and
to forecast them for the PSP mission. The frequency distributions for the
solar-wind key parameters magnetic field strength, proton velocity, density,
and temperature, are represented by lognormal functions, considering the
velocity distribution's bi-componental shape. Functional relations to the SSN
are compiled using OMNI data and based on data from both Helios probes, the
parameters' frequency distributions are fitted with respect to solar distance.
Thus, an empirical solar-wind model for the inner heliosphere is derived,
accounting for solar activity and solar distance. The inclusion of SSN
predictions and the extrapolation down to PSP's perihelion region enables us to
estimate the solar-wind environment for PSP's planned trajectory during its
mission duration. This empirical model yields estimated solar-wind values for
PSP's 1st perihelion in 2018 at 0.16 au: 87 nT, 340 km s-1, 214 cm-3 and 503000
K. The estimates for PSP's first closest perihelion, occurring in 2024 at 0.046
au, are 943 nT, 290 km s-1, 2951 cm-3, and 1930000 K. Since the modeled
velocity and temperature values below approximately 20 Rs appear overestimated
in comparison with existing observations, this suggests that PSP will directly
measure solar-wind acceleration and heating processes below 20 Rs as planned.Comment: 14 pages, 14 figures, 4 tables, accepted for publication in A&
Experimental results for the Poincar\'e center problem (including an Appendix with Martin Cremer)
We apply a heuristic method based on counting points over finite fields to
the Poincar\'e center problem. We show that this method gives the correct
results for homogeneous non linearities of degree 2 and 3. Also we obtain new
evidence for Zoladek's conjecture about general degree 3 non linearitiesComment: 16 pages, 2 figures, source code of programs at
http://www-ifm.math.uni-hannover.de/~bothmer/strudel/. Added references, the
result of Example 6.2 is not new. Added two new sections on rationally
reversible systems. The 4th codim 7 component we saw only experimentally can
now also be identified geometrical
Significance of log-periodic signatures in cumulative noise
Using methods introduced by Scargle in 1978 we derive a cumulative version of
the Lomb periodogram that exhibits frequency independent statistics when
applied to cumulative noise. We show how this cumulative Lomb periodogram
allows us to estimate the significance of log-periodic signatures in the S&P
500 anti-bubble that started in August 2000.Comment: 14 pages, 7 figures; AMS-Latex; introduction rewritten, some points
of the exposition clarified. Author-supplied PDF file with high resolution
graphics is available at http://btm8x5.mat.uni-bayreuth.de/~bothmer
Geometric Syzygies of Canonical Curves of even Genus lying on a K3-Surface
Based on a recent result of Voisin [2001] we describe the last nonzero syzygy
space in the linear strand of a canonical curve C of even genus g=2k lying on a
K3 surface, as the ambient space of a k-2-uple embedded P^{k+1}. Furthermore
the geometric syzygies constructed by Green and Lazarsfeld [1984] from
g^1_{k+1}'s form a non degenerate configuration of finitely many rational
normal curves on this P^{k+1}. This proves a natural generalization of Green's
conjecture [1984], namely that the geometric syzygies should span the space of
all syzygies, in this case.Comment: 29 pages; 5 figure
Geometric syzygies of elliptic normal curves and their secant varieties
We show that the linear syzygy spaces of elliptic normal curves, their secant
varieties and of bielliptic canonical curves are spanned by geometric syzygies.Comment: 31 Pages; AMSlate
Degenerations of Gushel-Mukai fourfolds, with a view towards irrationality proofs
We study a certain class of degenerations of Gushel-Mukai fourfolds as conic
bundles, which we call tame degenerations and which are natural if one wants to
prove that very general Gushel-Mukai fourfolds are irrational using the
degeneration method due to Voisin, Colliot-Th\'{e}l\`{e}ne-Pirutka, Totaro et
al. However, we prove that no such tame degenerations do exist.Comment: 25 page
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