MSRI - Toric Varieties

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)

Important

Additional Lodging information

Directions to MSRI

Schedule
Monday, June 15, 2009
9:30AM - 10:30AM	David Cox	Toric Varieties lecture 1 [Video available]
11:00AM - 12:00PM	David Cox	Toric Varieties lecture 2 [Video available]
Tuesday, June 16, 2009
9:30AM - 10:30AM	David Cox	Toric Varieties lecture 3 [Video available]
11:00AM - 12:00PM	David Cox	Toric Varieties lecture 4 [Video available]
Wednesday, June 17, 2009
9:30AM - 10:30AM	David Cox	Toric Varieties lecture 5 [Video available]
11:00AM - 12:00PM	David Cox	Toric Varieties lecture 6 [Video available]
Thursday, June 18, 2009
9:30AM - 10:30AM	David Cox	Toric Varieties lecture 7 [Video available]
11:00AM - 12:00PM	David Cox	Toric Varieties lecture 8 [Video available]
Friday, June 19, 2009
9:30AM - 10:30AM	David Cox	Toric Varieties lecture 9 [Video available]
Monday, June 22, 2009
9:30AM - 10:30AM	David Cox	Toric Varieties lecture 10 [Video available]
11:00AM - 12:00PM	David Cox	Toric Varieties lecture 11 [Video available]
Tuesday, June 23, 2009
9:30AM - 10:30AM	David Cox	Toric Varieties lecture 12 [Video available]
11:00AM - 12:00PM	David Cox	Toric Varieties lecture 13 [Video available]
Wednesday, June 24, 2009
9:30AM - 10:30AM	David Cox	Toric Varieties lecture 14 [Video available]
11:00AM - 12:00PM	David Cox	Toric Varieties lecture 15 [Video available]
2:00PM - 3:00PM	David Eisenbud	Toric Varieties- D. Eisenbud [Video available]
Thursday, June 25, 2009
9:30AM - 10:30AM	David Cox	Toric Varieties lecture 16 [Video available]
11:00AM - 12:00PM	David Cox	Toric Varieties lecture 17 [Video available]
2:00PM - 3:00PM	Matthias Beck	Toric Varieties- M. Beck [Video available]
Friday, June 26, 2009
9:30AM - 10:30AM	David Cox	Toric Varieties lecture 18 [Video available]
11:00AM - 12:00PM	David Cox	Toric Varieties lecture 19 [Video available]
2:00PM - 3:00PM	Sam Payne	Toric Varieties- S. Payne [Video available]

Questions about this workshop should be sent either by email to 455@msri.org
or by regular mail to:

Toric Varieties Mathematical Sciences Research Institute 17 Gauss Way, Berkeley, CA 94720-5070. USA

The Institute is committed to the principles of Equal Opportunity and Affirmative Action.