##### Department of Mathematics,

University of California San Diego

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### Algebraic Geometry Seminar

## Sofia Tirabassi

#### University of Utah

## Toward a Higher Dimensional Matsusaka-Ran Criterion

##### Abstract:

A conjecture of Debarre predicts that the only subvarieties of ppav with minimal cohomology class are Brill-Noether loci in Jacobians and the Fano surface of line in the intermediate Jacobian of a cubic three fold. We present a work in progress with Luigi Lombardi in which we made some progress toward the conjecture. In particular we give a generalization to higher dimension of Matsusaka-Ran criterion.

### January 10, 2014

### 1:00 PM

### AP&M 7218

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