Quasismooth hypersurfaces in toric varieties
Paola Comparin (Universidad de La Frontera, Temuco)
Aula Beltrami – Mercoledì 3 Luglio 2019 h.14:30
Abstract. According to Cox’s construction, any normal projective toric variety can be described as U//G, where U is an open subset in an affine space A^r and G an abelian group. Let Y be a hypersurface in X, defined as the zero set of a homogeneous polynomial in the Cox ring of X, with general coefficients. We call Y quasismooth if the intersection of its singular locus with U is empty, or equivalently, if the singular points of Y are in the irrelevant locus of X. In a joint work with M. Artebani and R. Guilbot, we study quasismoothness for hypersurfaces in toric variety and we give a characterization of it using combinatorial properties of the Newton polytope of the hypersurface, as well as relations with mirror constructions.