Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book
covers the standard topics in toric geometry; a novel feature is that each of the first nine …

We use the gauged linear sigma model introduced by Witten to calculate instanton
expansions for correlation functions in topological sigma models with target space a toric …

The purpose of this paper isto explain one extension of the ideas of the Griffiths-Dolgachev-
Steenbrink method for describing the Hodge theory of smooth (resp. quasi-smooth) …

The notion of quantum cohomology ring of a Kahler manifold V naturally appears in
theoretical physics in the consideration of the so called topological sigma model associated …

1. Introduction. The study ofinfinitesimal variations of Hodge structure on cohomology of
algebraicvarieties developed by J. Carlson, M. Green, P. Griffiths, and J. Harris has been …

The biregular classification of smooth d-dimensional toric Fano varieties is equivalent to the
classification of special simplicial polyhedra P in ℝ d, the so-called Fano polyhedra, up to an …

In this paper we show that conifold transitions between Calabi-Yau 3-folds can be used for
the construction of mirror manifolds and for the computation of the instanton numbers of …

Using combinatorial dualities for reflexive polyhedra and Gorenstein cones together with the
theory of generalized GKZ-hypergeometric functions, one can extend the calculation of the …

The purpose of this paper is to give basic tools for the classification of non singular toric
Fano verieties by means of the notions of primitive collections and primitive relations due to …

The absolute regularity of a Fano variety, denoted by reg^(X), is the largest dimension of the
dual complex of a log Calabi–Yau structure on X. The absolute coregularity is defined to be …