2,180 research outputs found
Upper bounds for regularized determinants
Let be a holomorphic vector bundle on a compact K\"ahler manifold . If
we fix a metric on , we get a Laplace operator acting upon
smooth sections of over . Using the zeta function of , one
defines its regularized determinant . We conjectured elsewhere
that, when varies, this determinant remains bounded from
above.
In this paper we prove this in two special cases. The first case is when
is a Riemann surface, is a line bundle and , and the second case is when is the projective line, is a line
bundle, and all metrics under consideration are invariant under rotation around
a fixed axis.Comment: 22 pages, plain Te
On the arithmetic Chern character
We consider a short sequence of hermitian vector bundles on some arithmetic
variety. Assuming that this sequence is exact on the generic fiber we prove
that the alternated sum of the arithmetic Chern characters of these bundles is
the sum of two terms, namely the secondary Bott Chern character class of the
sequence and its Chern character with supports on the finite fibers. Next, we
compute these classes in the situation encountered by the second author when
proving a "Kodaira vanishing theorem" for arithmetic surfaces
Semipurity of tempered Deligne cohomology
In this paper we define the formal and tempered Deligne cohomology groups,
that are obtained by applying the Deligne complex functor to the complexes of
formal differential forms and tempered currents respectively. We then prove the
existence of a duality between them, a vanishing theorem for the former and a
semipurity property for the latter. The motivation of these results comes from
the study of covariant arithmetic Chow groups. The semi-purity property of
tempered Deligne cohomology implies, in particular, that several definitions of
covariant arithmetic Chow groups agree for projective arithmetic varieties
The deformation complex is a homotopy invariant of a homotopy algebra
To a homotopy algebra one may associate its deformation complex, which is
naturally a differential graded Lie algebra. We show that infinity
quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation
complexes by an explicit construction.Comment: A revised version. The final version will appear in the volume
"Current Developments and Retrospectives in Lie Theory
Do negative random shocks affect trust and trustworthiness?
We report data from a variation of the trust game aimed at determining whether (and how) inequality and random shocks that affect wealth influence the levels of trust and trustworthiness. To tease apart the effect of the shock and the inequality, we compare behavior in a trust game where the inequality is initially given and one where it is the result of a random shock that reduces the second mover’s endowment. We find that first-movers send less to second-movers but only when the inequality results from a random shock. As for the amount returned, second-movers return less when they are endowed less than first-movers, regardless of whether the difference in endowments was initially given or occurred after a random shock
Trust and trustworthiness after negative random shocks
We experimentally investigate the effect of a negative endowment shock that can cause inequality in a trust game. Our goal is to assess whether different causes of inequality have different effects on trust and trustworthiness. In our trust game, we vary whether there is inequality (in favor of the second mover) or not and whether the inequality results from a random negative shock (i.e., the outcome of a die roll) or exists from the outset. Our findings suggest that inequality causes first-movers to send more of their endowment and second-movers to return more. However, we do not find support for the hypothesis that the cause of the inequality matters. Behavior after the occurrence of a random shock is not significantly different from the behavior in treatments where the inequality exists from the outset. Our results highlight the need to be cautious when interpreting the effects on trust and trustworthiness of negative random shocks in the field (such as natural disasters). Our results suggest that these effects are primarily driven by the inequality caused by the shock and not by any of the additional characteristics of the shock, like saliency or uncertainty
Melting and Pressure-Induced Amorphization of Quartz
It has recently been shown that amorphization and melting of ice were
intimately linked. In this letter, we infer from molecular dynamics simulations
on the SiO2 system that the extension of the quartz melting line in the
metastable pressure-temperature domain is the pressure-induced amorphization
line. It seems therefore likely that melting is the physical phenomenon
responsible for pressure induced amorphization. Moreover, we show that the
structure of a "pressure glass" is similar to that of a very rapidly (1e+13 to
1e+14 kelvins per second) quenched thermal glass.Comment: 9 pages, 4 figures, LaTeX2
There is no degree map for 0-cycles on Artin stacks
We show that there is no way to define degrees of 0-cycles on Artin stacks
with proper good moduli spaces so that (i) the degree of an ordinary point is
non-zero, and (ii) degrees are compatible with closed immersions.Comment: 3 page
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