3,345 research outputs found
Motivic zeta function via dlt modification
Given a smooth variety and a regular function on it, by considering
the dlt modification, we define the dlt motivic zeta function which does not depend on the choice of the dlt modification.Comment: 11 page
Starshaped locally convex hypersurfaces with prescribed curvature and boundary
In this paper we find strictly locally convex hypersurfaces in
with prescribed curvature and boundary. The main result is
that if the given data admits a strictly locally convex radial graph as a
subsolution, we can find a radial graph realizing the prescribed curvature and
boundary. As an application we show any smooth domain on the boundary of a
compact strictly convex body can be deformed to a smooth hypersurface with the
same boundary (inside the convex body) and realizing any prescribed curvature
function smaller than the curvature of the body.Comment: 24 pages. References updated. Published in The Journal of Geometric
Analysi
Is Meat the New Tobacco? Regulating Food Demand in the Age of Climate Change
Switching from a meat-heavy to a plant-based diet is one of the highest-impact lifestyle changes for climate mitigation and adaptation. Conventional demand-side energy policy has focused on increasing consumption of efficient machines and fuels. Regulating food demand has key advantages. First, food consumption is biologically constrained, thus switching to more efficient foods avoids unintended consequences of switching to more efficient machines, like higher overall energy consumption. Second, food consumption, like smoking, is primed for norm- shifting because it occurs in socially conspicuous environments. While place-based bans and information regulation were essential in lowering the prevalence of smoking, the same strategies may be even more effective in reducing meat demand. Several policy reforms can be implemented at the federal level, from reform of food marketing schemes to publicly subsidized meal programs
The essential skeleton of a degeneration of algebraic varieties
In this paper, we explore the connections between the Minimal Model Program
and the theory of Berkovich spaces. Let be a field of characteristic zero
and let be a smooth and proper -variety with semi-ample canonical
divisor. We prove that the essential skeleton of coincides with the
skeleton of any minimal -model and that it is a strong deformation retract
of the Berkovich analytification of . As an application, we show that the
essential skeleton of a Calabi-Yau variety over is a pseudo-manifold.Comment: To appear in American Journal of Mathematic
Poles of maximal order of motivic zeta functions
We prove a 1999 conjecture of Veys, which says that the opposite of the log
canonical threshold is the only possible pole of maximal order of Denef and
Loeser's motivic zeta function associated with a germ of a regular function on
a smooth variety over a field of characteristic zero. We apply similar methods
to study the weight function on the Berkovich skeleton associated with a
degeneration of Calabi-Yau varieties. Our results suggest that the weight
function induces a flow on the non-archimedean analytification of the
degeneration towards the Kontsevich-Soibelman skeleton.Comment: to appear in Duke Mathematical Journa
On the Feasibility of Linear Interference Alignment for MIMO Interference Broadcast Channels with Constant Coefficients
In this paper, we analyze the feasibility of linear interference alignment
(IA) for multi-input-multi-output (MIMO) interference broadcast channel
(MIMO-IBC) with constant coefficients. We pose and prove the necessary
conditions of linear IA feasibility for general MIMO-IBC. Except for the proper
condition, we find another necessary condition to ensure a kind of irreducible
interference to be eliminated. We then prove the necessary and sufficient
conditions for a special class of MIMO-IBC, where the numbers of antennas are
divisible by the number of data streams per user. Since finding an invertible
Jacobian matrix is crucial for the sufficiency proof, we first analyze the
impact of sparse structure and repeated structure of the Jacobian matrix.
Considering that for the MIMO-IBC the sub-matrices of the Jacobian matrix
corresponding to the transmit and receive matrices have different repeated
structure, we find an invertible Jacobian matrix by constructing the two
sub-matrices separately. We show that for the MIMO-IBC where each user has one
desired data stream, a proper system is feasible. For symmetric MIMO-IBC, we
provide proper but infeasible region of antenna configurations by analyzing the
difference between the necessary conditions and the sufficient conditions of
linear IA feasibility.Comment: 14 pages, 3 figures, accepted by IEEE Trans. on Signal Processin
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