The anticanonical complex for non-degenerate toric complete intersections

TL;DR

This paper extends the concept of the anticanonical complex to non-degenerate toric complete intersections, providing a classification of terminal Fano threefolds embedded in fake weighted projective spaces.

Contribution

It develops the theory of the anticanonical complex for non-degenerate systems and applies it to classify certain Fano threefolds in toric geometry.

Findings

Classification of terminal Fano threefolds in fake weighted projective spaces

Extension of the anticanonical complex to non-degenerate complete intersections

New tools for studying Fano varieties with torus actions

Abstract

The anticanonical complex generalizes the Fano polytope from toric geometry and has been used to study Fano varieties with torus action so far. We work out the case of complete intersections in toric varieties defined by non-degenerate systems of Laurent polynomials. As an application, we classify the terminal Fano threefolds that are embedded into a fake weighted projective space via a general system of Laurent polynomials.