Algebraic geometry is one of the most diverse fields of research in
mathematics. It has had an incredible evolution over the past
century, with new subfields constantly branching off and
spectacular progress in certain directions, and at the same time,
with many fundamental unsolved problems still to be tackled. In the
spring of 2009 the first main workshop of the MSRI algebraic
geometry program served as an introductory panorama of current
progress in the field, addressed to both beginners and experts.
This volume reflects that spirit, offering expository overviews of
the state of the art in many areas of algebraic geometry.
Prerequisites are kept to a minimum, making the book accessible to
a broad range of mathematicians. Many chapters present approaches
to long-standing open problems by means of modern techniques
currently under development and contain questions and conjectures
to help spur future research.
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