This two volume work on Positivity in Algebraic Geometry contains a contemporary account
of a body of work in complex algebraic geometry loosely centered around the theme of …

Transcendental methods of algebraic geometry have been extensively studied since a very
long time, starting with the work of Abel, Jacobi and Riemann in the nineteenth century …

The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts
with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on …

Systems of polynomial equations are a common occurrence in problem formulations in
engineering, science, and mathematics. Solution sets of such systems, ie, algebraic sets, are …

This introductive chapter is mainly a review of the basic tools and concepts which will be
employed in the rest of the book: differential forms, currents, holomorphic and …

Holomorphic vector bundles have become objects of interest not only to algebraic and
differential geometers and complex analysts but also to low dimensional topologists and …

Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as
metric aspects. The subject is on the crossroad of algebraic and differential geometry …

Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate
relationship between Sasakian and Kähler geometries, especially when the Kähler structure …

Written by the founders of the new and expanding field of numerical algebraic geometry, this
is the first book that uses an algebraic-geometric approach to the numerical solution of …

Introduction M. Kodaira's vanishing theorem, saying that the inverse of an ample invert ible
sheaf on a projective complex manifold X has no cohomology below the dimension of X and …