Algebraic Geometry Working Seminar | Francisco Villacis | Linear Amoebas and their Combinatorial Properties

A projective toric variety \(X\Sigma\) comes with a moment map \(\mu\), whose image is a convex polytope that encodes a lot of the geometry of \(X\Sigma\). These moment maps and their associated polytopes have played a fundamental role in quantization programs and mirror symmetry. One natural question when studying these maps is whether the image \(\mu(X)\) also encodes geometric information of a subvariety \(X\subset X_\Sigma\). In this talk, we introduce combinatorial objects that let us study this image, called the (compactified) amoeba of \(X\), in the case where \(X\) is a linear subspace of projective space.

MC 5403