Chapter 9

Complex spaces and modifications7C326140E164

Reduced and unibranch spaces, modifications, and analytic extension.

Sections and subsections

1. 9.1 Complex spaces and modificationsB64C7FEAE2E7
2. 9.2 Division and finite analytic modulesD4E6B7455291
3. 9.3 Analytic sets and their local branchesA49B7CFC7FBF
4. 9.4 Reduced spaces and normalizationC16A2F5D9879
5. 9.5 Analytic curves and finite maps2BDD13613B99
6. 9.6 Blowups and resolution25A311AD092F
7. 9.7 Proper images and relative principalization05BF24D5DFA6
8. 9.8 Connected fibers and resolution modelsF0CABED1A01F
9. 9.9 Plurisubharmonic functions on reduced spaces75F10F3C1577
10. 9.10 Pluripotential theory on unibranch spaces5131A8B4E30A
    1. 9.10.1 Complex spaces089901B2844A
    2. 9.10.11 Plurisubharmonic functions04B4AD1F512D
    3. 9.10.17 Extensions of the results in the smooth settingCE1C14C908CB
11. 9.11 Potentials and equations on unibranch spaces77EFAFB55325
    1. 9.11.1 Potentials and disk tests0753019C64C3
    2. 9.11.4 Descent through a resolution65930026730A
    3. 9.11.6 Envelopes and normalized compactness29C5C6037D7D
    4. 9.11.8 Ideal envelopes defined on resolutions491CF8180F3F
    5. 9.11.10 Boundary weights on a quotient surface6B078FD09EA1
    6. 9.11.16 Adapted monomial tests on affine toric spaces73BE0E663644
    7. 9.11.24 Extended measures and finite damping449B961AB405
    8. 9.11.27 Equations on projective cones821709E49BC3
    9. 9.11.30 Logarithmic poles at the vertexF23187DC5D42
    10. 9.11.41 The bounded equation750E47668A22
    11. 9.11.47 The quadric cone07FD7FBC796C
    12. 9.11.50 Logarithmic equations on normalized curves7AADE341B54C
    13. 9.11.56 A projective cusp with a degenerate pullback90D7DAC242DE
    14. 9.11.59 A logarithmic endpoint for integrable dataE2DBF02EA6E5
    15. 9.11.63 Nonclosed equations on cuspidal products25867983D80D