Complete singular collineations and quadrics

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.

arXiv comment23 pages. Exposition improved and proof of Proposition 4.1 simplified thanks to the comments of the referee. Added a section on the positivity of the anti-canonical divisor of the compactifications. arXiv admin note: text overlap with arXiv:2012.13999