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**Lecture:** Tuesday and Thursday, 13:15 – 14:30, Physics Building 227

**Name:** Prof. Ezra Miller (you should call me "Ezra")
**Address:** Mathematics Department,
Duke University, Box 90320,
Durham, NC 27708-0320
**Office:** Physics 209
**Phone:** (919) 660-2846
**Email:** *ezramath.duke.edu*
**Webpage:**
*http://math.duke.edu/~ezra*
**Course webpage:** you're already looking at it...
but it's *http://math.duke.edu/~ezra/273/273.html*
**Office hours:**Thursday, 14:30 – 16:00, Physics 209

- sheaves
- spectrum of a ring
- schemes (affine, projective, neither)
- types of schemes (reduced, normal, factorial, regular)
- morphisms of schemes: immersions, finiteness conditions
- quasicoherent sheaves
- fiber products
- affine and projective morphisms
- separated and proper morphisms
- line bundles

- Tentative due dates for the homework assignments this semester are listed in the table below. You will have approximately two weeks to do each assignment.
**All solutions you turn in must be typewritten.**Communicating your ideas is an integral part of being a mathematician. It is essential that you learn this skill in graduate school. In addition to the usual PDF files, I will provide the LaTeX source files for each of the homework assignments. You should feel free to use (or not) these as LaTeX templates for your solutions, by simply filling in your responses in those files. I will be happy to answer any questions you might have about LaTeX, although you might want to ask your classmates first.**Turn in your printed homework solutions to me in class, and send electronic versions to me**. Send at least your .tex file (I may comment on your TeX usage); if you include your .pdf file as well then it can serve as verification that your system produces the same thing as mine does.**Print your typed solutions double-sided.**This will save paper and lighten the stack of papers that I have to carry around.**I encourage collaboration on homework**, as long as each person understands the solutions, writes them up using their own words, and indicates—on the homework page—who their collaborators were.**You must cite sources in your solutions.**If you rely on so-and-so's theorem, then you must state the theorem and tell me where you found it. Be specific: "the local-ringed spaces proposition" is not precise; in contrast, "[Vakil, Proposition 7.3.1]" is. (Even better would be, "a key result on morphisms of affine schemes as local-ringed spaces [Vakil, Proposition 7.3.1]".) Theorems are often known by many names, so I'm likely not to recognize many theorems by names you might attach.**Late homework will not be accepted.**Early homework is fine: leave the hard copies in my mailbox in the Math Department.- Homework solutions should be thoroughly explained: there will be no credit for unsupported answers.

Assignment | Due Date | Problems |
---|---|---|

Homework #1 |
Tue. 14 September | in PDF or LaTeX |

Homework #2 |
Tue. 28 September | in PDF or LaTeX |

Homework #3 |
Thu. 14 October | in PDF or LaTeX |

Homework #4 |
Tue. 26 October | in PDF or LaTeX |

Homework #5 |
Tue. 9 November | in PDF or LaTeX |

Homework #6 |
Thu. 9 December | in PDF or LaTeX |

Level | Title | Author(s) | Publisher, date |
---|---|---|---|

Lower | Algebraic Geometry, a first course | Harris | Springer, 1995 |

Comparable | Algebraic Geometry | Hartshorne | Springer, 1977 |

Comparable | The Geometry of Schemes | Eisenbud & Harris | Springer, 2000 |

Comparable | Principles of Algebraic Geometry | Griffiths & Harris | Wiley, 1978 |

- list of all courses given in the Math Department in Fall 2010.
- Official University calendar for academic year 2010–2011.
- Fundamental University policies concerning academic dishonesty and related matters.

Many thanks are due to Jeremy Martin and Vic Reiner, who provided templates for this webpage.

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by Duke University.

*ezramath.duke.edu*

*Mon Oct 25 23:53:00 EDT 2010*

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