\relax \@writefile{toc}{\contentsline {chapter}{\numberline {1}Linear systems of curves}{13}} \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \newlabel{ch:1}{{1}{13}} \@writefile{toc}{\contentsline {section}{\numberline {1.1}Linear pencils}{13}} \newlabel{sec:1.1}{{1.1}{13}} \newlabel{eq1}{{1.1}{13}} \newlabel{eq2}{{1.2}{14}} \newlabel{eq3}{{1.3}{14}} \@writefile{toc}{\contentsline {section}{\numberline {1.2}Irrational pencils}{15}} \newlabel{sec:1.2}{{1.2}{15}} \@writefile{toc}{\contentsline {section}{\numberline {1.3}Linear systems}{16}} \newlabel{sec:1.3}{{1.3}{16}} \newlabel{eqa1}{{1.4}{16}} \@writefile{toc}{\contentsline {section}{\numberline {1.4}The characteristic property of linear systems}{18}} \newlabel{sec:1.4}{{1.4}{18}} \@writefile{toc}{\contentsline {section}{\numberline {1.5}Extension of the theorems of Bertini}{19}} \newlabel{sec:1.5}{{1.5}{19}} \@writefile{toc}{\contentsline {section}{\numberline {1.6}The image surfaces of linear systems}{20}} \newlabel{sec:1.6}{{1.6}{20}} \@writefile{toc}{\contentsline {paragraph}{Note}{22}} \@writefile{toc}{\contentsline {section}{\numberline {1.7}Equivalent curves and complete linear systems}{22}} \newlabel{sec:1.7}{{1.7}{22}} \@writefile{toc}{\contentsline {section}{\numberline {1.8}Sum and difference of linear systems: the residue theorem}{25}} \newlabel{sec:1.8}{{1.8}{25}} \@writefile{toc}{\contentsline {paragraph}{Note}{26}} \@writefile{toc}{\contentsline {paragraph}{Remark}{27}} \@writefile{toc}{\contentsline {paragraph}{NOTE}{27}} \@writefile{toc}{\contentsline {section}{\numberline {1.9}The image surface of the sum system}{28}} \newlabel{sec:1.9}{{1.9}{28}} \@writefile{toc}{\contentsline {section}{\numberline {1.10}Virtual characters}{29}} \newlabel{sec:1.10}{{1.10}{29}} \@writefile{toc}{\contentsline {section}{\numberline {1.11}Exceptional curves}{31}} \newlabel{sec:1.11}{{1.11}{31}} \@writefile{toc}{\contentsline {section}{\numberline {1.12}A note on the reducible exceptional curves}{35}} \newlabel{sec:1.12}{{1.12}{35}} \@writefile{toc}{\contentsline {section}{\numberline {1.13}The virtual characteristic series}{38}} \newlabel{sec:1.13}{{1.13}{38}} \@writefile{toc}{\contentsline {paragraph}{Note}{38}} \@setckpt{1}{ \setcounter{page}{39} \setcounter{equation}{4} \setcounter{enumi}{3} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{18} \setcounter{mpfootnote}{0} \setcounter{part}{0} \setcounter{chapter}{1} \setcounter{section}{13} \setcounter{subsection}{0} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{figure}{0} \setcounter{table}{0} \setcounter{Corollary}{0} \setcounter{Theorem}{0} \setcounter{Lemma}{1} }