Curve singularities

An Algebraic and Geometric approach

This book presents a treatment of curve singularities, a subject of renewed actuality. Curve singularities become a fundamental tool in recent developments as arc spaces, resolution of singularities, base point of linear systems, valuation theory or coding theory.

Rational branches, parameterizations, Hamburger-Noether matrices, resolution of singularities, Arf closure and saturation are specially developed on an algebraic basis. On the other hand, exceptional divisors and combinatorial configurations obtained by blowing ups, proximity relations, infinitely near points and linear systems obtained from them are also developed on a geometric basis. Ground fields are arbitrary perfect fields. All together gives an algebraic geometric insight of singular points of curves, which can have any embedding dimension.

The book is addressed to researchers as well as to postgraduate students interested on the topic or related areas.