The lecture begins with two nice combinatorial problems as an introduction to free arrangements and the corresponding vector bundles. Free arrangements are shown to be contingent on the exponents of the restricted multiarrangement. The Euler sequence gives a vector bundle theoretic definition of freeness. Results of the correspondence of free arrangement to vector bundles are summarized. In particular, the Edelman and Riener conjecture is proven by this correspondence and results of H. Terao

Keywords:

Extended Catalan arrangement; cone of Shi arrangement; free arrangements; vector bundles; splitting of vector bundle

Lecture #10658

Need help? Visit our help pages at http://www.msri.org/communications/vmath/hints

Supplements

Right click on the link and "Save As..." to save to your local computer.

• 10658.pdf (0.1 MB)

Left click on thumbnail to see a larger image.

Streaming Video

This is a high quality streaming video encoded with MPEG-4 and with 640x480 resolution.

Windows and Mac users, QuickTime 6.5 or later required
Linux users, please see our Linux Help Page on how to view our streaming videos

Follow this link to --- Watch the Video Now Via Streaming Video ---

Download QuickTime File

You can download the QuickTime file here. Right click on the link and "Save As..." to save to your local computer.

• 10658-10658-QuickTime.mov (452 MB)

Create a DVD

You can download the video and audio files here. Please note that you need both files to create a DVD. Right click on the link and "Save As..." to save to your local computer. You can find instructions on how to create a DVD on our help page at http://www.msri.org/communications/vmath/author

• 10658-10658-DVD PCM Audio.aiff (709 MB - Audio Only)
• 10658-10658-MPEG-2 120min High Quality Encode.m2v (1615 MB - Video Only)

Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture.

If you would like to purchase a copy of this video for $15+shipping, please Click Here!

See more of our Streaming Videos on our main VMath - Streaming Video page.