English

Complete singular collineations and quadrics

Algebraic Geometry 2022-09-22 v3

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.

Keywords

Cite

@article{arxiv.2111.02940,
  title  = {Complete singular collineations and quadrics},
  author = {Alex Casarotti and Elsa Corniani and Alex Massarenti},
  journal= {arXiv preprint arXiv:2111.02940},
  year   = {2022}
}

Comments

23 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

R2 v1 2026-06-24T07:26:20.213Z