In theory there is no difference between theory and practice. In practice there is. Yogi Berra
A SINGULAR Introduction to Commutative Algebra offers a rigorous intro duction to …

Singularity theory is a field of intensive study in modern mathematics with fascinating
relations to algebraic geometry, complex analysis, commutative algebra, representation …

Even the simplest singularities of planar curves, eg where the curve crosses itself, or where
it forms a cusp, are best understood in terms of complex numbers. The full treatment uses …

This comprehensive and self-contained exposition of the algebro-geometric theory of
singularities of plane curves covers both the classical and modern aspects of the field. It …

We develop a simple and efficient algorithm to compute Riemann–Roch spaces of divisors
in general algebraic function fields which does not use the Brill–Noether method of adjoints …

A study of the relation between a noetherian local domain with a given valuation and its
associated graded ring with respect to the valuation, which in some cases is an esentially …

AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

We study Abhyankar valuations of excellent equicharacteristic local domains with an
algebraically closed residue field. For zero dimensional valuations we prove that whenever …

Systems of polynomial equations are central to mathematics and its application to science
and engineering. Their solution sets, called algebraic sets, are studied in algebraic …

We give an explicit description of the semigroup of values of a plane curve singularity with
several branches in terms of the usual invariants of the equisingularity type in the sense of …