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Summer Graduate School

Toric Varieties June 15, 2009 - June 26, 2009
Organizers David Cox ( Amherst College) and Hal Schenck (University of Illinois)
Lecturer(s) No Lecturers Assigned Yet.
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Description

Toric varieties are algebraic varieties defined by combinatorial data, and there is a wonderful interplay between algebra, combinatorics and geometry involved in their study. Many of the key concepts of abstract algebraic geometry (for example, constructing a variety by gluing affine pieces) have very concrete interpretations in the toric case, making toric varieties an ideal tool for introducing students to abstruse concepts.

The first week will cover basic material, including affine toric varieties, projective toric varieties, normal toric varieties constructed from fans, divisors, and homogeneous coordinates. We will also discuss toric surfaces.The second week will go deeper into the subject, covering topics such as ampleness, vanishing theorems in cohomology, the secondary fan, and geometric invariant theory.

An important feature of the workshop is that it does not assume that students have a full background in algebraic geometry. Students will need to know basic facts about varieties in affine and projective space, but we assume no knowledge of schemes, sheaves, cohomology, etc.

Bibliography (PDF 13KB)


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Schedule
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Jun 15, 2009
Monday
09:30 AM - 10:30 AM
  Toric Varieties lecture 1
David Cox (University of Massachusetts, Amherst)
11:00 AM - 12:00 PM
  Toric Varieties lecture 2
David Cox (University of Massachusetts, Amherst)
Jun 16, 2009
Tuesday
09:30 AM - 10:30 AM
  Toric Varieties lecture 3
David Cox (University of Massachusetts, Amherst)
11:00 AM - 12:00 PM
  Toric Varieties lecture 4
David Cox (University of Massachusetts, Amherst)
Jun 17, 2009
Wednesday
09:30 AM - 10:30 AM
  Toric Varieties lecture 5
David Cox (University of Massachusetts, Amherst)
11:00 AM - 12:00 PM
  Toric Varieties lecture 6
David Cox (University of Massachusetts, Amherst)
Jun 18, 2009
Thursday
09:30 AM - 10:30 AM
  Toric Varieties lecture 7
David Cox (University of Massachusetts, Amherst)
11:00 AM - 12:00 PM
  Toric Varieties lecture 8
David Cox (University of Massachusetts, Amherst)
Jun 19, 2009
Friday
09:30 AM - 10:30 AM
  Toric Varieties lecture 9
David Cox (University of Massachusetts, Amherst)
Jun 22, 2009
Monday
09:30 AM - 10:30 AM
  Toric Varieties lecture 10
David Cox (University of Massachusetts, Amherst)
11:00 AM - 12:00 PM
  Toric Varieties lecture 11
David Cox (University of Massachusetts, Amherst)
Jun 23, 2009
Tuesday
09:30 AM - 10:30 AM
  Toric Varieties lecture 12
David Cox (University of Massachusetts, Amherst)
11:00 AM - 12:00 PM
  Toric Varieties lecture 13
David Cox (University of Massachusetts, Amherst)
Jun 24, 2009
Wednesday
09:30 AM - 10:30 AM
  Toric Varieties lecture 14
David Cox (University of Massachusetts, Amherst)
11:00 AM - 12:00 PM
  Toric Varieties lecture 15
David Cox (University of Massachusetts, Amherst)
02:00 PM - 03:00 PM
  Toric Varieties- D. Eisenbud
David Eisenbud (MSRI - Mathematical Sciences Research Institute)
Jun 25, 2009
Thursday
09:30 AM - 10:30 AM
  Toric Varieties lecture 16
David Cox (University of Massachusetts, Amherst)
11:00 AM - 12:00 PM
  Toric Varieties lecture 17
David Cox (University of Massachusetts, Amherst)
02:00 PM - 03:00 PM
  Toric Varieties- M. Beck
Matthias Beck (San Francisco State University)
Jun 26, 2009
Friday
09:30 AM - 10:30 AM
  Toric Varieties lecture 18
David Cox (University of Massachusetts, Amherst)
11:00 AM - 12:00 PM
  Toric Varieties lecture 19
David Cox (University of Massachusetts, Amherst)
02:00 PM - 03:00 PM
  Toric Varieties- S. Payne
Sam Payne (Yale University)