%PDF-1.4 % 4 0 obj << /S /GoTo /D (Abstract.0) >> endobj 7 0 obj (Abstract) endobj 8 0 obj << /S /GoTo /D (Contents.0) >> endobj 11 0 obj (Table of Contents) endobj 12 0 obj << /S /GoTo /D (chapter*.2) >> endobj 15 0 obj (Notation) endobj 16 0 obj << /S /GoTo /D (part.1) >> endobj 19 0 obj (I Regular del Pezzo surfaces with irregularity) endobj 20 0 obj << /S /GoTo /D (chapter.1) >> endobj 23 0 obj (1 Introduction) endobj 24 0 obj << /S /GoTo /D (section.1.1) >> endobj 27 0 obj (1.1 Regular varieties) endobj 28 0 obj << /S /GoTo /D (section.1.2) >> endobj 31 0 obj (1.2 New results) endobj 32 0 obj << /S /GoTo /D (section.1.3) >> endobj 35 0 obj (1.3 Motivation from the minimal model program) endobj 36 0 obj << /S /GoTo /D (section.1.4) >> endobj 39 0 obj (1.4 Regular forms and the classification of del Pezzo surfaces) endobj 40 0 obj << /S /GoTo /D (section.1.5) >> endobj 43 0 obj (1.5 A prior example) endobj 44 0 obj << /S /GoTo /D (section.1.6) >> endobj 47 0 obj (1.6 A brief outline) endobj 48 0 obj << /S /GoTo /D (chapter.2) >> endobj 51 0 obj (2 Numerical bounds on del Pezzo surfaces with irregularity) endobj 52 0 obj << /S /GoTo /D (section.2.1) >> endobj 55 0 obj (2.1 L-torsors) endobj 56 0 obj << /S /GoTo /D (section.2.2) >> endobj 59 0 obj (2.2 Normal del Pezzo surfaces of local complete intersection) endobj 60 0 obj << /S /GoTo /D (chapter.3) >> endobj 63 0 obj (3 Algebraic foliations on regular varieties) endobj 64 0 obj << /S /GoTo /D (section.3.1) >> endobj 67 0 obj (3.1 Quotients by foliations) endobj 68 0 obj << /S /GoTo /D (section.3.2) >> endobj 71 0 obj (3.2 Foliations in characteristic two) endobj 72 0 obj << /S /GoTo /D (chapter.4) >> endobj 75 0 obj (4 The construction of regular del Pezzo surfaces with irregularity) endobj 76 0 obj << /S /GoTo /D (section.4.1) >> endobj 79 0 obj (4.1 The set-up) endobj 80 0 obj << /S /GoTo /D (section.4.2) >> endobj 83 0 obj (4.2 An example of degree one) endobj 84 0 obj << /S /GoTo /D (section.4.3) >> endobj 87 0 obj (4.3 An example of degree two) endobj 88 0 obj << /S /GoTo /D (section.4.4) >> endobj 91 0 obj (4.4 Geometric reducedness) endobj 92 0 obj << /S /GoTo /D (chapter.5) >> endobj 95 0 obj (5 A geometric description of the surface of degree one) endobj 96 0 obj << /S /GoTo /D (section.5.1) >> endobj 99 0 obj (5.1 Normalization of geometric base change) endobj 100 0 obj << /S /GoTo /D (section.5.2) >> endobj 103 0 obj (5.2 Local ring of functions) endobj 104 0 obj << /S /GoTo /D (section.5.3) >> endobj 107 0 obj (5.3 An equation defining the singular locus) endobj 108 0 obj << /S /GoTo /D (section.5.4) >> endobj 111 0 obj (5.4 The geometry of the singular locus) endobj 112 0 obj << /S /GoTo /D (chapter.6) >> endobj 115 0 obj (6 Future research directions) endobj 116 0 obj << /S /GoTo /D (part.2) >> endobj 119 0 obj (II Intersection numbers on quotients in geometric invariant theory) endobj 120 0 obj << /S /GoTo /D (chapter.7) >> endobj 123 0 obj (7 Introduction) endobj 124 0 obj << /S /GoTo /D (section.7.1) >> endobj 127 0 obj (7.1 A brief history) endobj 128 0 obj << /S /GoTo /D (section.7.2) >> endobj 131 0 obj (7.2 The main goal) endobj 132 0 obj << /S /GoTo /D (section.7.3) >> endobj 135 0 obj (7.3 New results) endobj 136 0 obj << /S /GoTo /D (chapter.8) >> endobj 139 0 obj (8 Lifting classes on smooth varieties) endobj 140 0 obj << /S /GoTo /D (section.8.1) >> endobj 143 0 obj (8.1 Geometric invariant theory) endobj 144 0 obj << /S /GoTo /D (section.8.2) >> endobj 147 0 obj (8.2 Lifts) endobj 148 0 obj << /S /GoTo /D (section.8.3) >> endobj 151 0 obj (8.3 Vanishing on Kirwan strata) endobj 152 0 obj << /S /GoTo /D (section.8.4) >> endobj 155 0 obj (8.4 Vanishing over an algebraically closed field) endobj 156 0 obj << /S /GoTo /D (section.8.5) >> endobj 159 0 obj (8.5 Torsion over an arbitrary field) endobj 160 0 obj << /S /GoTo /D (chapter.9) >> endobj 163 0 obj (9 Singular varieties and strictly semi-stable points) endobj 164 0 obj << /S /GoTo /D (section.9.1) >> endobj 167 0 obj (9.1 Construction) endobj 168 0 obj << /S /GoTo /D (section.9.2) >> endobj 171 0 obj (9.2 Integration) endobj 172 0 obj << /S /GoTo /D (section.9.3) >> endobj 175 0 obj (9.3 Application) endobj 176 0 obj << /S /GoTo /D (chapter.10) >> endobj 179 0 obj (10 Invariance of the GIT integration ratio) endobj 180 0 obj << /S /GoTo /D (section.10.1) >> endobj 183 0 obj (10.1 Chow class) endobj 184 0 obj << /S /GoTo /D (section.10.2) >> endobj 187 0 obj (10.2 Maximal torus) endobj 188 0 obj << /S /GoTo /D (section.10.3) >> endobj 191 0 obj (10.3 Linearized variety) endobj 192 0 obj << /S /GoTo /D (chapter.11) >> endobj 195 0 obj (11 Direct products and central extensions) endobj 196 0 obj << /S /GoTo /D (section.11.1) >> endobj 199 0 obj (11.1 Direct products) endobj 200 0 obj << /S /GoTo /D (section.11.2) >> endobj 203 0 obj (11.2 Central extensions) endobj 204 0 obj << /S /GoTo /D (chapter.12) >> endobj 207 0 obj (12 A computation for groups of type An) endobj 208 0 obj << /S /GoTo /D (chapter.13) >> endobj 211 0 obj (13 Generalization) endobj 212 0 obj << /S /GoTo /D (part*.3) >> endobj 215 0 obj (Bibliography) endobj 216 0 obj << /S /GoTo /D (part*.5) >> endobj 219 0 obj (Appendix) endobj 220 0 obj << /S /GoTo /D (appendix.A) >> endobj 223 0 obj (A Chow groups and quotient stacks) endobj 224 0 obj << /S /GoTo /D (section.A.1) >> endobj 227 0 obj (A.1 Chow groups) endobj 228 0 obj << /S /GoTo /D (section.A.2) >> endobj 231 0 obj (A.2 Operational Chow groups) endobj 232 0 obj << /S /GoTo /D [233 0 R /FitH ] >> endobj 235 0 obj << /Length 479 /Filter /FlateDecode >> stream xmRMs0W((胯#e )m5SlRg_q]v}죚=,Y(%3)EA j/q9rKz1N5%T|IdiQvz$[8'D # H3%RUgПm7 U*35ٍsp%TE:*_̴6$L=ɼp"_-Òz$bjD!7`$Hwa>V'v\8WZxSuf5mHQMH(b`,?N03ķõQѶFdN1@iw8M?צק2v[R럽|ttZ"vxشݥ{;ZwXZchZrxWZ #P Ե&r^_?_9?ȥ& y6&p,}s82"DPc/D!1r[;j9} endstream endobj 233 0 obj << /Type /Page /Contents 235 0 R /Resources 234 0 R /MediaBox [0 0 612 792] /Parent 240 0 R >> endobj 236 0 obj << /D [233 0 R /XYZ 89 721 null] >> endobj 237 0 obj << /D [233 0 R /XYZ 90 684.134 null] >> endobj 234 0 obj << /Font << /F26 238 0 R /F15 239 0 R >> /ProcSet [ /PDF /Text ] >> endobj 243 0 obj << /Length 187 /Filter /FlateDecode >> stream xU=0dHWFPLbQ"m.!ܽyeK@ dIWU X˝[sK02ɦnkL?`RE9V*\1(KjD/YL D^|TT$Ԍ+7N.[VG_g3@j endstream endobj 242 0 obj << /Type /Page /Contents 243 0 R /Resources 241 0 R /MediaBox [0 0 612 792] /Parent 240 0 R >> endobj 244 0 obj << /D [242 0 R /XYZ 89 721 null] >> endobj 241 0 obj << /Font << /F15 239 0 R /F27 245 0 R >> /ProcSet [ /PDF /Text ] >> endobj 248 0 obj << /Length 1618 /Filter /FlateDecode >> stream xuَ6=_GUIa?nآ@6}%f!8_߹$k'qч~Mv8KW*0ߥHBվZ<|a~&0NM ~6z,9͏~pG]г|ΙPkgJ+cu[.LwB")?a[Mۮ+-^$ o;yl6t5|YHVH'5wWcvէuPVݟMx4Ti#QB :)vhl']U4`!Xn(E MyeEB<Ӡ욋ތu QrLjvOamOm[rRD 98 #Py]oUG#D(fE^#
nSMA7<}#Em0כ<.èK]gYォ~-)3;&!G*
JѰYgꊞI" o=O5X@!qDFƚxH1X,*`Y!5%sX>I,e3j꼰]kRV\ +TDh7?ӟ!*a:X$ՂMŨjv./6[
#/;9@r*ZoS(XQA'(;韀o!y /h֛5&|I[jĤ{G>xoaz 0o~'`ŌKvvi= f~XÞrDXqᾚ#r,ЉY=vAvݔ*֖1蒕99cSsbL990ܠ <[gnSnܺqƳn#dƞgɖB?"[Ոu/N!jt:R
mkNE$j!NבFugVEQ;} -lh#FTS'XM&PPI\PFp_=E3a,XB$ -XG7:ma飃$/͠B4R)= Ʉ<G zM^[`βTs/H#yn