##### Department of Mathematics,

University of California San Diego

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### Algebraic geometry seminar

## Dr. Giovanni Inchiostro

#### University of Washington

## Degenerations of twisted maps to algebraic stacks

##### Abstract:

Assume that one has a family of nodal curves over the punctured disc C^*\to \Delta^*, with a morphism C^*\to \calM to an algebraic stack \calM with a projective good moduli space. I will explain how one can, up to replacing the punctured disc with a ramified cover of it, compactify this family to a family of nodal (twisted) curves over the whole disc C\to \Delta, in a way such that the generic morphism C^*\to \calM extends to C.

For example, in the case where \calM = BPGL_n, this gives a recipe to extend fibrations in Brauer-Severi varieties, whereas for \calM = [A^1/Gm] this gives a way to extend families of line bundles with a section. The talk is based on a joint work with Andrea Di Lorenzo.

### April 28, 2023

### 3:30 PM

https://ucsd.zoom.us/j/

Meeting ID: 950 3948 6629

Research Areas

Algebraic Geometry****************************