Complete singular collineations and quadrics

TL;DR

This paper constructs compactifications of spaces of linear and symmetric maps using blow-ups of secant varieties, exploring their geometry and connections to degree two stable maps.

Contribution

It introduces new compactifications of linear map spaces via blow-ups of secant varieties, linking them to stable map spaces.

Findings

Constructed compactifications of linear and symmetric map spaces.

Analyzed the birational geometry of these compactifications.

Explored relations with spaces of degree two stable maps.

Abstract

We construct wonderful compactifications of the spaces of linear maps, and symmetric linear maps of a given rank as blow-ups of secant varieties of Segre and Veronese varieties. Furthermore, we investigate their birational geometry and their relations with some spaces of degree two stable maps.