These notes deal with deformation theory of complex analytic singularities and related
objects. The first part treats general theory. The central notion is that of versal deformation in …

O teorema de Hilbert-Burch fornece uma boa descriçao de variedades determinantais de
codimensao dois e de suas deformaçoes em termos da matriz de representaçao. Neste …

In 1891 Hurwitz published a conjecture yielding the number of topological types of rational
functions on C1 with xed orders of poles and xed critical values assuming the functions …

We survey determinantal singularities, their deformations, and their topology. This class of
singularities generalizes the well studied case of complete intersections in several different …

Let R be a polynomial ring and M a finitely generated graded R-module of maximal grade
(which means that the ideal I t (A) generated by the maximal minors of a homogeneous …

We describe a method for computing discriminants for a large class of families of isolated
determinantal singularities–families induced by perturbations of matrices. The approach …

In this paper we study the moduli stack U _ 1, n^ ns U 1, nns of curves of arithmetic genus 1
with n marked points, forming a nonspecial divisor. In Polishchuk (A modular …

A closed subscheme $ X\subset\mathbb {P}^ n $ is said to be determinantal if its
homogeneous saturated ideal can be generated by the $ s\times s $ minors of a …

In this work, the classification of simple isolated Cohen-Macaulay codimension 2
singularities is generalized to a non-complete classification of simple non-isolated Cohen …

A scheme X⊂ Pn of codimension c is called standard determinantal if its homogeneous
saturated ideal can be generated by the t× t minors of a homogeneous t×(t+ c− 1) matrix (fij) …