Algebraic Geometry over the Complex Numbers

Authors:

ISBN: 978-1-4614-1808-5 (Print) 978-1-4614-1809-2 (Online)

Table of contents (19 chapters)

  1. Front Matter

    Pages i-xii

  2. Introduction through Examples

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-17

      Plane Curves

  3. Sheaves and Geometry

    1. Front Matter

      Pages 19-19

    2. No Access

      Book Chapter

      Pages 21-47

      Manifolds and Varieties via Sheaves

    3. No Access

      Book Chapter

      Pages 49-78

      More Sheaf Theory

    4. No Access

      Book Chapter

      Pages 79-96

      Sheaf Cohomology

    5. No Access

      Book Chapter

      Pages 97-115

      De Rham Cohomology of Manifolds

    6. No Access

      Book Chapter

      Pages 117-136

      Riemann Surfaces

    7. No Access

      Book Chapter

      Pages 137-153

      Simplicial Methods

  4. Hodge Theory

    1. Front Matter

      Pages 155-155

    2. No Access

      Book Chapter

      Pages 157-167

      The Hodge Theorem for Riemannian Manifolds

    3. No Access

      Book Chapter

      Pages 169-177

      Toward Hodge Theory for Complex Manifolds

    4. No Access

      Book Chapter

      Pages 179-188

      Kähler Manifolds

    5. No Access

      Book Chapter

      Pages 189-201

      A Little Algebraic Surface Theory

    6. No Access

      Book Chapter

      Pages 203-221

      Hodge Structures and Homological Methods

    7. No Access

      Book Chapter

      Pages 223-236

      Topology of Families

    8. No Access

      Book Chapter

      Pages 237-251

      The Hard Lefschetz Theorem

  5. Coherent Cohomology

    1. Front Matter

      Pages 253-253

    2. No Access

      Book Chapter

      Pages 255-264

      Coherent Sheaves

    3. No Access

      Book Chapter

      Pages 265-277

      Cohomology of Coherent Sheaves

    4. No Access

      Book Chapter

      Pages 279-291

      Computation of Some Hodge Numbers

    5. No Access

      Book Chapter

      Pages 293-304

      Deformations and Hodge Theory

  6. Analogies and Conjectures

    1. Front Matter

      Pages 305-305

    2. No Access

      Book Chapter

      Pages 307-320

      Analogies and Conjectures

  7. Back Matter

    Pages 321-329