The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new...

This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry...

This book provides an introduction to abstract algebraic geometry. The prerequisites for this approach are results from commutative algebra, which are stated as needed, and some elementary topology. There are more than 400 exercises...