Preface.- 1. Plane Curves.- 2. Manifolds and Varieties via Sheaves.- 3. More Sheaf Theory.- 4. Sheaf Cohomology.- 5. de Rham Cohomoloy of Manifolds.- 6. Riemann Surfaces.- 7. Simplicial Methods.- 8. The Hodge Theorem for Riemann Manifolds.- 9. Toward Hodge Theory for Complex Manifolds.- 10. Kahler Manifolds.- 11. A Little Algebraic Surface Theory.- 12. Hodge Structures and Homological Methods.- 13. Topology of Families.- 14. The Hard Lefschez Theorem.- 15. Coherent Sheaves.- 16. Computation of Coherent Sheaves.- 17. Computation of some Hodge numbers.- 18. Deformation Invariance of Hodge Numbers.- 19. Analogies and Conjectures.- References.- 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:“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, and … it may serve as an excellent guide to the great standard texts in the field.” (Werner Kleinert, Zentralblatt MATH, Vol. 1235, 2012)
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