Abstract:
We consider exponential tropical varieties, which appear as analogues
of algebraic tropical varieties when we pass from algebraic varieties
to varieties given by zero sets of systems of exponential sums. We
describe a construction of exponential tropical varieties arising
from the action of the complex Monge–Ampère operator on piecewise-linear
functions and show that every such variety can be obtained
in this way. As an application, we deduce a criterion
for the vanishing of the value of the mixed Monge–Ampère operator.
This is an analogue and generalization of the criterion for the vanishing
of the mixed volume of convex bodies.
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