In this paper we present an effective method for linearizing rational varieties of codimension at least two under Cremona transformations, starting from a given parametrization. Using these linearizing Cremonas, we simplify the equations of secant and tangential varieties of some classical examples, including Veronese, Segre and Grassmann varieties. We end the paper by treating the special case of the Segre embedding of the n-fold product of projective spaces, where cumulant Cremonas, arising from algebraic statistics, appear as specific cases of our general construction.

Ciliberto, C., Angelica Cueto, M., Mella, M., Ranestad, K., Zwiernik, P. (2016). Cremona linearizations of some classical varieties. In A.C. G. Casnati (a cura di), ``From Classical to Modern Algebraic Geometry'' (pp. 375-407). Springer [10.1007/978-3-319-32994-9_9].

Cremona linearizations of some classical varieties

C. Ciliberto
;
2016-01-01

Abstract

In this paper we present an effective method for linearizing rational varieties of codimension at least two under Cremona transformations, starting from a given parametrization. Using these linearizing Cremonas, we simplify the equations of secant and tangential varieties of some classical examples, including Veronese, Segre and Grassmann varieties. We end the paper by treating the special case of the Segre embedding of the n-fold product of projective spaces, where cumulant Cremonas, arising from algebraic statistics, appear as specific cases of our general construction.
2016
Settore MAT/03 - GEOMETRIA
English
Rilevanza internazionale
Articolo scientifico in atti di convegno
Birational maps; Cremona transformations; Cumulants; Secant cumulants; Segre and Veronese varieties;
Ciliberto, C., Angelica Cueto, M., Mella, M., Ranestad, K., Zwiernik, P. (2016). Cremona linearizations of some classical varieties. In A.C. G. Casnati (a cura di), ``From Classical to Modern Algebraic Geometry'' (pp. 375-407). Springer [10.1007/978-3-319-32994-9_9].
Ciliberto, C; Angelica Cueto, M; Mella, M; Ranestad, K; Zwiernik, P
Contributo in libro
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/227422
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 7
social impact