2013/02/05 by Houston, Kevin, Atique, Roberta Wik
#58K40 #58K50 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1302.1104
The classification of map-germs up to the natural right-left equivalence (also known as A-equivalence) is often complicated. Certainly it is more complicated than K-equivalence which is extremely easy to work with because the associated tangent spaces are not 'mixed' modules as they are in the A-equivalence case. In this paper we use a version of K-equivalence, denoted VK-equivalence, that is defined using K-equivalences that preserve a variety in the source of maps to classify maps up to A-equivalence. This is possible through making clear the connection between the two equivalences - previous work by Damon mostly focussed on the relation between the codimensions associated to the maps. To demonstrate the power and efficiency of the method we give a classification of certain Ae-codimension 2 maps from n-space to n+1-space. The proof using VK-equivalence is considerably shorter - by a wide margin - than one using A-equivalence directly.