Algebraic Geometry over the Complex Numbers

Preface
Part 1. A Quick Tour
1. Plane Curves
Part 2. Sheaves and Geometry
2. Manifolds and Varieties via Sheaves
3. Basic Sheaf Theory
4. Sheaf Cohomology
5. De Rham Cohomoloy of Manifolds
6. Riemann Surfaces
7. Simplicial Methods
Part 3. Hodge Theory
8. The Hodge Theorem for Riemann Manifolds
9. Toward Hodge Theory for Complex Manifolds
10. Kahler Manifolds
11. Homological Methods in Hodge Theory
12. A Little Algebraic Surface Theory
13. Topology of Families
14. The Hard Lefschez Theorem
Part 4. Coherent Cohomology
15. Coherent Sheaves on Projective Space
16. Computation of Some Hodge Numbers
17. Deformation Invariance of Hodge Numbers
Part 5. A Glimpse Beyond
18. Analogies and Conjectures
Bibliography
Index

Donu Arapura is a Professor of Mathematics at Purdue University. He received his Ph.D. from Columbia University in 1985. Dr. Arapura's primary research includes algebraic geometry, and he has written and co-written several publications ranging from Hodge cycles to cohomology.

From the reviews:

"Book provides a very lucid, vivid, and versatile first introduction to algebraic geometry, with strong emphasis on its transcendental aspects. The author provides a broad panoramic view of the subject, illustrated with numerous instructive examples and interlarded with a wealth of hints for further reading. Indeed, the balance between rigor, intuition, and completeness in the presentation of the material is absolutely reasonable for such an introductory course book, and ... it may serve as an excellent guide to the great standard texts in the field." (Werner Kleinert, Zentralblatt MATH, Vol. 1235, 2012)

"Masterful mathematical expositors guide readers along a meaningful journey. ... Every student should read this book first before grappling with any of those bibles. ... This is an advanced book in its own right ... . Arapura's knack for doing things in the simplest possible way and explaining the 'why' makes for much easier reading than one might reasonably expect. Summing Up: Highly recommended. Upper-division undergraduates and above." (D. V. Feldman, Choice, Vol. 50 (5), January, 2013)

"The book under review is a welcome addition to the literature on complex algebraic geometry. The approach chosen by the author balances the algebraic and transcendental approaches and unifies them by using sheaf theoretical methods. ... This is a well-written text ... with plenty of examples to illustrate the ideas being discussed." (Felipe Zaldivar, The Mathematical Association of America, June, 2012)

From the reviews:

"The book under review evolved from various courses in algebraic geometry the author taught at Purdue University. It is intended for graduate level courses on algebraic geometry over C. ... Every section of each chapter ends with a series of exercises that complement the treated material, sometimes asking to give proofs of stated results. ... This work can serve as a textbook in an introductory course in algebraic geometry with a strong emphasis on its transcendental aspects, or as a reference book on the subject." (Pietro De Poi, Mathematical Reviews, June, 2013)

"Masterful mathematical expositors guide readers along a meaningful journey. ... Every student should read this book first before grappling with any of those bibles. ... This is an advanced book in its own right ... . Arapura's knack for doing things in the simplest possible way and explaining the 'why' makes for much easier reading than one might reasonably expect. Summing Up: Highly recommended. Upper-division undergraduates and above." (D. V. Feldman, Choice, Vol. 50 (5), January, 2013)

"The book under review is a welcome addition to the literature on complex algebraic geometry. The approach chosen by the author balances the algebraic and transcendental approaches and unifies them by using sheaf theoretical methods. ... This is a well-written text ... with plenty of examples to illustrate the ideas being discussed." (Felipe Zaldivar, The Mathematical Association of America, June, 2012)

"Book provides a very lucid, vivid, and versatile first introduction to algebraic geometry, with strong emphasis on its transcendental aspects. The author provides a broad panoramic view of the subject, illustrated with numerous instructive examples and interlarded with a wealth of hints for further reading. Indeed, the balance between rigor, intuition, and completeness in the presentation of the material is absolutely reasonable for suchan introductory course book,