Variables can only be used in XPath in place of a value, not in place of an arbitrary part of the expression text. (They are like variables in Java or C#, not like variables in a shell script.)
So you want
page/selected/*[name()=$FieldName]/@min
Michael Kay
http://www.saxonica.com/
Author, XSLT 2.0 and XPath 2.0 Programmer's Reference