669 research outputs found
Points of Low Height on Elliptic Curves and Surfaces, I: Elliptic surfaces over P^1 with small d
For each of n=1,2,3 we find the minimal height h^(P) of a nontorsion point P
of an elliptic curve E over C(T) of discriminant degree d=12n (equivalently, of
arithmetic genus n), and exhibit all (E,P) attaining this minimum. The minimal
h^(P) was known to equal 1/30 for n=1 (Oguiso-Shioda) and 11/420 for n=2
(Nishiyama), but the formulas for the general (E,P) were not known, nor was the
fact that these are also the minima for an elliptic curve of discriminant
degree 12n over a function field of any genus. For n=3 both the minimal height
(23/840) and the explicit curves are new. These (E,P) also have the property
that that mP is an integral point (a point of naive height zero) for each
m=1,2,...,M, where M=6,8,9 for n=1,2,3; this, too, is maximal in each of the
three cases.Comment: 15 pages; some lines in the TeX source are commented out with "%" to
meet the 15-page limit for ANTS proceeding
Classification of Singular Fibres on Rational Elliptic Surfaces in Characteristic Three
We determine and list all possible configurations of singular fibres on
rational elliptic surfaces in characteristic three. In total, we find that 267
distinct configurations exist. This result complements Miranda and Persson's
classification in characteristic zero, and Lang's classification in
characteristic two.Comment: 40 Pages. Minor typos correcte
L-functions with large analytic rank and abelian varieties with large algebraic rank over function fields
The goal of this paper is to explain how a simple but apparently new fact of
linear algebra together with the cohomological interpretation of L-functions
allows one to produce many examples of L-functions over function fields
vanishing to high order at the center point of their functional equation. The
main application is that for every prime p and every integer g>0 there are
absolutely simple abelian varieties of dimension g over Fp(t) for which the BSD
conjecture holds and which have arbitrarily large rank.Comment: To appear in Inventiones Mathematica
Shimura curve computations via K3 surfaces of Neron-Severi rank at least 19
It is known that K3 surfaces S whose Picard number rho (= rank of the
Neron-Severi group of S) is at least 19 are parametrized by modular curves X,
and these modular curves X include various Shimura modular curves associated
with congruence subgroups of quaternion algebras over Q. In a family of such K3
surfaces, a surface has rho=20 if and only if it corresponds to a CM point on
X. We use this to compute equations for Shimura curves, natural maps between
them, and CM coordinates well beyond what could be done by working with the
curves directly as we did in ``Shimura Curve Computations'' (1998) =
Comment: 16 pages (1 figure drawn with the LaTeX picture environment); To
appear in the proceedings of ANTS-VIII, Banff, May 200
Non-liftable Calabi-Yau spaces
We construct many new non-liftable three-dimensional Calabi-Yau spaces in
positive characteristic. The technique relies on lifting a nodal model to a
smooth rigid Calabi-Yau space over some number field as introduced by the first
author and D. van Straten.Comment: 16 pages, 5 tables; v2: minor corrections and addition
Anomaly Cancelation in Field Theory and F-theory on a Circle
We study the manifestation of local gauge anomalies of four- and
six-dimensional field theories in the lower-dimensional Kaluza-Klein theory
obtained after circle compactification. We identify a convenient set of
transformations acting on the whole tower of massless and massive states and
investigate their action on the low-energy effective theories in the Coulomb
branch. The maps employ higher-dimensional large gauge transformations and
precisely yield the anomaly cancelation conditions when acting on the one-loop
induced Chern-Simons terms in the three- and five-dimensional effective theory.
The arising symmetries are argued to play a key role in the study of the
M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact
that all fully resolved F-theory geometries inducing multiple Abelian gauge
groups or non-Abelian groups admit a certain set of symmetries, we are able to
generally show the cancelation of pure Abelian or pure non-Abelian anomalies in
these models.Comment: 48 pages, 2 figures; v2: typos corrected, comments on circle fluxes
adde
F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
The Mordell-Weil group of an elliptically fibered Calabi-Yau threefold X
contains information about the abelian sector of the six-dimensional theory
obtained by compactifying F-theory on X. After examining features of the
abelian anomaly coefficient matrix and U(1) charge quantization conditions of
general F-theory vacua, we study Calabi-Yau threefolds with Mordell-Weil
rank-one as a first step towards understanding the features of the Mordell-Weil
group of threefolds in more detail. In particular, we generate an interesting
class of F-theory models with U(1) gauge symmetry that have matter with both
charges 1 and 2. The anomaly equations --- which relate the Neron-Tate height
of a section to intersection numbers between the section and fibral rational
curves of the manifold --- serve as an important tool in our analysis.Comment: 29 pages + appendices, 5 figures; v2: minor correction
Different mechanism of two-proton emission from proton-rich nuclei Al and Mg
Two-proton relative momentum () and opening angle ()
distributions from the three-body decay of two excited proton-rich nuclei,
namely Al p + p + Na and Mg p
+ p + Ne, have been measured with the projectile fragment separator
(RIPS) at the RIKEN RI Beam Factory. An evident peak at MeV/c as
well as a peak in around 30 are seen in the two-proton
break-up channel from a highly-excited Mg. In contrast, such peaks are
absent for the Al case. It is concluded that the two-proton emission
mechanism of excited Mg is quite different from the Al case, with
the former having a favorable diproton emission component at a highly excited
state and the latter dominated by the sequential decay process
Comparative effectiveness of alternative intervals between first and second doses of the mRNA COVID-19 vaccines
The optimal interval between the first and second doses of COVID-19 mRNA vaccines has not been thoroughly evaluated. Employing a target trial emulation approach, we compared the effectiveness of different interdose intervals among >6 million mRNA vaccine recipients in Georgia, USA, from December 2020 to March 2022. We compared three protocols defined by interdose interval: recommended by the Food and Drug Administration (FDA) (17-25 days for Pfizer-BioNTech; 24-32 days for Moderna), late-but-allowable (26-42 days for Pfizer-BioNTech; 33-49 days for Moderna), and late ( ≥ 43 days for Pfizer-BioNTech; ≥50 days for Moderna). In the short-term, the risk of SARS-CoV-2 infection was lowest under the FDA-recommended protocol. Longer-term, the late-but-allowable protocol resulted in the lowest risk (risk ratio on Day 120 after the first dose administration compared to the FDA-recommended protocol: 0.83 [95% confidence interval: 0.82-0.84]). Here, we showed that delaying the second dose by 1-2 weeks may provide stronger long-term protection
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