The anticanonical complex for non-degenerate toric complete intersections

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.

arXiv comment27 pages, further resuls added

References in corpus (8)

• Canonical toric Fano threefolds
• Bounds on Fake Weighted Projective Space
• Toric Fano 3-folds with terminal singularities
• Log terminal singularities, platonic tuples and iteration of Cox rings
• On terminal Fano 3-folds with 2-torus action
• On torus actions of higher complexity
• On the anticanonical complex
• On Fano threefolds with ${\mathbb{C}}^{\ast }$-action

Cited by in corpus (2)

• On smooth Fano fourfolds of Picard number two
• Classifying log del Pezzo surfaces with torus action