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%%%%%% Math 273 Homework \#1, Fall 2010 %%%%%%
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%%%%%% Instructor: Ezra Miller %%%%%%
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\title{\mbox{}\\[-8ex]Math 273 Homework \#1, Fall 2010\\\normalsize
Instructor: Ezra Miller}
\author{Solutions by: ...your name...\\[2ex]
Collaborators: ...list those with whom you worked on this assignment...\\[1ex]}
\date{Due: Tuesday 14 September 2010}
\maketitle
\vspace{-3ex}%
\noindent
\textsc{Reading assignments} in \cite{vakil}\vspace{-.5ex}
\begin{itemize}
\item%
by Tuesday 7 September: \S3.1, \S3.2, \S3.3, \S3.4\vspace{-1ex}
\item%
by Thursday 9 September: \S3.5\vspace{-1ex}
\item%
by Tuesday 14 September: \S14.1, \S14.2.2, \S14.3.3, \S14.3.D\vspace{-1ex}
\item%
by Thursday 16 September: \S3.6, \S3.7
\end{itemize}
\noindent
\textsc{Exercises}:
In \cite{vakil}, exercises have labels C.S.N, for ``Chapter~C,
Section~S, Exercise~N'', where $\text{C},\text{S} \in \ZZ_+$ and
$\text{N} \in \text{A},\ldots,\text{Z}$. It is not expected that
everyone will complete all of the assigned exercises, but those marked
``[required]'' are essential.\vspace{-1ex}%
\begin{enumerate}
\item[3.2.C]%
\item[3.2.G]%
\begin{enumerate}
\item\mbox{}%
[required]
\item%
\item%
Demonstrate that 3.2.F is a special case of part~(a) by considering
the projection $Y \times X \to X$.
\end{enumerate}
\item[3.2.I\,\,]%
\item[3.3.B]%
[required] (Note: Most commonly, sheaf-hom is denoted using some form
of calligraphy or math italics, such as $\HHom(\cF,\cG)$, since
$\Hom(\cF,\cG)$ is most often interpreted as the group of
homomorphisms $\cF \to \cG$ between objects $\cF$ and $\cG$ in the
category of sheaves.)
\item[3.3.I\,\,]%
[required]
\item[3.4.E]%
[required]
\item[3.4.M]%
\item[3.4.P]%
[required]
\item[3.5.A]%
\item[3.5.B]%
\item[3.5.C]%
\item[3.5.E]%
[The part about the global section functor not being exact is required]
\item[3.5.F]%
[required]
\end{enumerate}
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\bibitem[Vakil]{vakil}
Ravi Vakil, \emph{Foundations of algebraic geometry}, notes dated
August 26, 2010.
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