| Introduction | p. 1 |
| Notation | p. 17 |
| Basic Notions and Ideas | |
| Splitting Deformations of Degenerations | p. 23 |
| Definitions | p. 23 |
| Splitting criteria via configuration of singular fibers | p. 30 |
| What is a barking? | p. 33 |
| Barking, I | p. 33 |
| Barking, II | p. 37 |
| Semi-Local Barking Deformations: Ideas and Examples | p. 41 |
| Semi-local example, I (Reduced barking) | p. 41 |
| Semi-local example, II (Multiple barking) | p. 46 |
| Semi-local example, III | p. 48 |
| Supplement: Numerical condition | p. 51 |
| Supplement: Example of computation of discriminant loci | p. 53 |
| Global Barking Deformations: Ideas and Examples | p. 57 |
| Preparation: Simplification lemmas | p. 57 |
| Typical examples of barking deformations | p. 60 |
| Supplement: Collision and Symmetry | p. 74 |
| Collision, I | p. 74 |
| Collision, II | p. 76 |
| Construction based on symmetry | p. 78 |
| Deformations of Tubular Neighborhoods of Branches | |
| Deformations of Tubular Neighborhoods of Branches (Preparation) | p. 85 |
| Branches | p. 85 |
| Deformation atlas | p. 87 |
| Subbranches | p. 89 |
| Dominant subbranches | p. 91 |
| Tame and wild subbranches | p. 93 |
| Supplement: Riemenschneider's work | p. 98 |
| Construction of Deformations by Tame Subbranches | p. 99 |
| Construction of deformations by tame subbranches | p. 99 |
| Supplement for the proof of Theorem 6.1.1 | p. 104 |
| Alternative construction | p. 104 |
| Generalization | p. 104 |
| Proportional subbranches | p. 107 |
| Singular fibers | p. 109 |
| Construction of Deformations of type Al | p. 119 |
| Deformations of type Al | p. 119 |
| Singular fibers | p. 124 |
| Supplement: Singularities of certain curves | p. 129 |
| Newton polygons and singularities | p. 137 |
| Construction of Deformations by Wild Subbranches | p. 143 |
| Deformations of ripple type | p. 144 |
| Singular fibers | p. 150 |
| Subbranches of Types Al, Bl, Cl | p. 153 |
| Subbranches of types Al, Bl, Cl | p. 153 |
| Demonstration of properties of type Al | p. 160 |
| Demonstration of properties of type Bl | p. 164 |
| Demonstration of properties of type Cl | p. 166 |
| Construction of Deformations of Type Bl | p. 177 |
| Deformations of type Bl | p. 178 |
| Singular fibers | p. 180 |
| Construction of Deformations of Type Cl | p. 183 |
| Waving polynomials | p. 183 |
| Waving sequences | p. 187 |
| Deformations of type Cl | p. 191 |
| Singular fibers | p. 198 |
| Supplement: The condition that u divides l | p. 200 |
| Proof of Lemma 11.5.1 | p. 203 |
| Recursive Construction of Deformations of Type Cl | p. 209 |
| Ascending, descending, and stable polynomials | p. 209 |
| Technical preparation I | p. 213 |
| Recursive construction I | p. 218 |
| Technical preparation II | p. 225 |
| Recursive construction II | p. 228 |
| Examples of non-recursive deformations of type Cl | p. 232 |
| Types Al, Bl, and Cl Exhaust all Cases | p. 235 |
| Results | p. 235 |
| Preparation | p. 236 |
| Case 1: b = 0 | p. 238 |
| Case 2: b ≥ 1 | p. 243 |
| Conclusion | p. 249 |
| Supplement: Proof of Lemma 13.4.4 | p. 249 |
| Construction of Deformations by Bunches of Subbranches | p. 253 |
| Propagation sequences | p. 253 |
| Bunches of subbranches | p. 255 |
| Example of a deformation by a wild bunch | p. 260 |
| Barking Deformations of Degenerations | |
| Construction of Barking Deformations (Stellar Case) | p. 265 |
| Linear degenerations | p. 265 |
| Deformation atlas | p. 267 |
| Crusts | p. 271 |
| Deformation atlas associated with one crust | p. 273 |
| Reduced barking | p. 275 |
| Simple Crusts (Stellar Case) | p. 279 |
| Deformation atlases associated with multiple crusts | p. 279 |
| Multiple barking | p. 281 |
| Criteria for splittability | p. 284 |
| Singularities of fibers | p. 288 |
| Application to a constellar case | p. 292 |
| Barking genus | p. 295 |
| Constraints on simple crusts | p. 299 |
| Compound barking (Stellar Case) | p. 303 |
| Crustal sets | p. 303 |
| Deformation atlas associated with a crustal set | p. 304 |
| Example of a crustal set | p. 306 |
| Deformations of Tubular Neighborhoods of Trunks | p. 309 |
| Trunks | p. 309 |
| Subtrunks, I | p. 311 |
| Subtrunks, II | p. 316 |
| Other constructions of deformations | p. 320 |
| Construction of Barking Deformations (Constellar Case) | p. 327 |
| Notation | p. 327 |
| Tensor condition | p. 329 |
| Multiple barking (constellar case) | p. 332 |
| Criteria for splittability | p. 342 |
| Looped trunks | p. 345 |
| Further Examples | p. 349 |
| Fake singular fibers | p. 349 |
| Splitting families which give the same splitting | p. 349 |
| Example 1 | p. 351 |
| Example 2 | p. 353 |
| Three different complete propagations | p. 357 |
| Example of a practical computation of a compound barking | p. 360 |
| Wild cores | p. 368 |
| Replacement and grafting | p. 370 |
| Increasing multiplicities of simple crusts | p. 377 |
| Singularities of Subordinate Fibers near Cores | |
| Singularities of Fibers around Cores | p. 383 |
| Branched coverings and ramification points | p. 385 |
| Singularities of fibers | p. 393 |
| Zeros of the plot function | p. 396 |
| The number of subordinate fibers and singularities | p. 400 |
| Discriminant functions and tassels | p. 404 |
| Determination of the singularities | p. 405 |
| Seesaw phenomenon | p. 413 |
| Supplement: The case m = ln | p. 417 |
| Arrangement Functions and Singularities, I | p. 421 |
| Arrangement polynomials | p. 422 |
| Vanishing cycles | p. 427 |
| Discriminants of arrangement polynomials | p. 430 |
| The coefficients of arrangement polynomials take arbitrary values | p. 432 |
| Arrangement Functions and Singularities, II | p. 439 |
| Theta function | p. 439 |
| Genus 1: Arrangement functions | p. 445 |
| Riemann theta functions and Riemann factorization | p. 449 |
| Genus ≥ 2: Arrangement functions | p. 455 |
| Supplement | p. 461 |
| Riemann theta function and related topics | p. 461 |
| Classification of Atoms of Genus ≤ 5 | |
| Classification Theorem | p. 483 |
| List of Weighted Crustal Sets for Singular Fibers of Genus ≤ 5 | p. 487 |
| Genus 1 | p. 492 |
| Stellar singular fibers, <$>A = {\op P}^1<$> | p. 492 |
| <$>I_n^{\ast}<$> | p. 496 |
| mIn | p. 496 |
| Genus 2 | p. 497 |
| Stellar singular fibers, <$>A = {\op P}^1<$> | p. 497 |
| Stellar singular fibers, genus(A) = 1 | p. 502 |
| Self-welding of stellar singular fibers of genus 1 | p. 503 |
| Genus 3 | p. 503 |
| Stellar singular fibers, <$>A = {\op P}^1<$> | p. 503 |
| Stellar singular fibers, genus(A) = 1, 2 | p. 518 |
| Self-welding of stellar singular fibers of genus 2 | p. 519 |
| Welding of stellar singular fibers of genus 2 and genus 1 | p. 520 |
| Genus 4 | p. 521 |
| Stellar singular fibers, <$>A = {\op P}^1<$> | p. 521 |
| Stellar singular fibers, genus(A) = 1, 2 | p. 541 |
| Self-welding and self-connecting of genus 3 or 2 | p. 543 |
| Welding of stellar singular fibers of genus 3 and genus 1 | p. 546 |
| Welding of stellar singular fibers of genus 2 and genus 2 | p. 546 |
| Welding of stellar singular fibers of genus 2, 1, and 1 | p. 547 |
| Genus 5 | p. 547 |
| Stellar singular fibers, <$>A = {\op P}^1<$> | p. 547 |
| Stellar singular fibers, genus(A) = 1, 2, 3 | p. 567 |
| Self-welding and self-connecting of genus 4 or 3 | p. 570 |
| Welding of stellar singular fibers of genus 4 and genus 1 | p. 574 |
| Welding of stellar singular fibers of genus 3 and genus 2 | p. 575 |
| Bibliography | p. 581 |
| Index | p. 587 |
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