## Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: A new residual intersection phenomenon

Seminar | March 6 | 3:45-5 p.m. | 939 Evans Hall

David Eisenbud, UC Berkeley

Department of Mathematics

Residual intersection theory works well for ideals like the ideal of $p\times p$ minors of a generic $p \times (p+1)$ matrix, but fails for some very nice ideals, such as the ideal of $2 \times 2$ minors of a $2\times n$ matrix for n greater than $3$. Poking around for what might be true, Bernd Ulrich and I stumbled on a new phenomenon that seems to be rather general. We are far from proving all that seems to be true, but I'll describe our conjectures and results, which at least cover the $2 \times n$ matrices. This is joint work of mine with Bernd Ulrich and Craig Huneke.

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