Contents
Introduction vi i
Chapter I . Preliminarie s 1
§1. Equisingularit y clas s of a branch. Modul i spac e 1
§2. Puiseu x expansio n 3
Chapter II . Equisingularit y Invariant s 5
§1. Th e semigrou p T = v(0) 5
§2. Conducto r an d differen t 7
§3. Th e characteristi c o f a branch 9
§4. Conducto r an d regula r differentia l form s o n C 13
§5. Regula r differentia l form s o n a plane algebrai c curv e 14
§6. Retur n t o th e loca l case 14
Chapter III . Parametrization s 19
§1. Shor t parametrizatio n o f a branch 19
§2. Th e spac e o f short parametrization s 2 0
§3. Th e dimensio n o f th e C vecto r spac e o f holomorphi c differentia l
forms modul o exac t form s 2 5
Chapter IV . Th e Modul i Spac e 2 9
§1. Noncompactnes s o f the modul i spac e fo r g 3 2 9
§2. Th e cas e g = 2 3
§3. Compactnes s o f th e modul i spac e o f a n equisingularit y clas s wit h
characteristic (4 ; 6, #2) 3 7
Chapter V . Example s 4 5
§1. n = 2 and 3 4 5
§2. (n; m = /?i ) = (4;5 ) 4 6
§3. 0 = 2 , (n;m,/32 ) = (4;6,& ) 4 7
§4. (n;m) = (5 ; 6) 4 7
§5. (n ; m) = (6 ; 7) 5 2
§6. Th e invarian t r(C) i n the clas s (6 ; 7) 6 1
§7. Topolog y o f the modul i spac e of the clas s (6 ; 7) 6 6
Chapter VI . Application s o f Deformation Theor y 7 3
§1. Introductio n 7 3
§2. Viewin g the proble m fro m th e perspectiv e o f Deformation Theor y 7 3
§3. O n th e dimensio n o f the generi c componen t o f the modul i spac e 8 0
Previous Page Next Page