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 …

The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

The closure of a discrete exponential family is described by a finite set of equations
corresponding to the circuits of an underlying oriented matroid. These equations are similar …

The image of the principal minor map for n× n-matrices is shown to be closed. In the 19th
century, Nanson and Muir studied the implicitization problem of finding all relations among …

The columns of an integral matrix D give rise to the toric variety VK (ID) and also provide a
parametrization of a subset of VK (ID), the so-called toric set ΓK (D). We completely …

Let IM and IN be defining ideals of toric varieties such that IM is a projection of IN, ie IN⊆ IM.
We give necessary and sufficient conditions for the equality IM= rad (IN+ (f1,…, fs)), where …

A complex manifold $ Y $ is said to have the interpolation property if a holomorphic map to $
Y $ from a subvariety $ S $ of a reduced Stein space $ X $ has a holomorphic extension to …

Let K be a field and let X (resp. X∗) be a subset of a projective space Ps− 1 (resp. affine
space As), over the field K, parameterized by rational functions. Let I (X)(resp. I (X∗)) be the …

In this thesis, we first study the problem of determining set theoretic complete intersection
(stci) projective monomial curves. We are also interested in finding the equations of the …

Dans ce travail, nous donnons une nouvelle méthode pour calculer les générateurs du
semigroupe de certains diviseurs positifs a support sur le diviseur exceptionnel d'une …