Quasismoooth hypersurfaces in toric varieties

TL;DR

This paper characterizes when monomial linear systems on toric varieties produce quasismooth hypersurfaces, using combinatorial data from Newton polytopes and exponent matrices, advancing understanding of hypersurface smoothness conditions.

Contribution

It offers a new combinatorial criterion for quasismoothness of hypersurfaces in toric varieties based on Newton polytopes and exponent matrices.

Findings

Provides a combinatorial characterization of quasismooth hypersurfaces

Relates quasismoothness to Newton polytope properties

Connects hypersurface smoothness to monomial basis exponents

Abstract

We provide a combinatorial characterization of monomial linear systems on toric varieties whose general member is quasismooth. This is given both in terms of the Newton polytope and in terms of the matrix of exponents of a monomial basis.