We study smooth integral curves of bidegree (1, 1), called smooth conics, in the flag threefold F. The study is motivated by the fact that the family of smooth conics contains the set of fibers of the twistor projection F → CP2. We give a bound on the maximum number of smooth conics contained in a smooth surface S ⊂ F. Then, we show qualitative properties of algebraic surfaces containing a prescribed number of smooth conics. Last, we study surfaces containing infinitely many twistor fibers. We show that the only smooth cases are surfaces of bidegree (1, 1). Then, for any integer a > 1, we exhibit a method to construct an integral surface of bidegree (a, a) containing infinitely many twistor fibers.

Surfaces in the flag threefold containing smooth conics and twistor fibers / Altavilla, Amedeo; Ballico, Edoardo; Brambilla Maria, Chiara. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5446. - STAMPA. - 19:(2022), pp. 28101-28119. [10.1007/s00009-022-02202-3]

Surfaces in the flag threefold containing smooth conics and twistor fibers

Ballico Edoardo
Co-primo
;
2022-01-01

Abstract

We study smooth integral curves of bidegree (1, 1), called smooth conics, in the flag threefold F. The study is motivated by the fact that the family of smooth conics contains the set of fibers of the twistor projection F → CP2. We give a bound on the maximum number of smooth conics contained in a smooth surface S ⊂ F. Then, we show qualitative properties of algebraic surfaces containing a prescribed number of smooth conics. Last, we study surfaces containing infinitely many twistor fibers. We show that the only smooth cases are surfaces of bidegree (1, 1). Then, for any integer a > 1, we exhibit a method to construct an integral surface of bidegree (a, a) containing infinitely many twistor fibers.
2022
Altavilla, Amedeo; Ballico, Edoardo; Brambilla Maria, Chiara
Surfaces in the flag threefold containing smooth conics and twistor fibers / Altavilla, Amedeo; Ballico, Edoardo; Brambilla Maria, Chiara. - In: MEDITERRANEAN JOURNAL OF MATHEMATICS. - ISSN 1660-5446. - STAMPA. - 19:(2022), pp. 28101-28119. [10.1007/s00009-022-02202-3]
File in questo prodotto:
File Dimensione Formato  
s00009-022-02202-3.pdf

Solo gestori archivio

Descrizione: first online
Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 460.14 kB
Formato Adobe PDF
460.14 kB Adobe PDF   Visualizza/Apri
s00009-022-02202-3.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 458.18 kB
Formato Adobe PDF
458.18 kB Adobe PDF   Visualizza/Apri

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/11572/360864
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
  • OpenAlex ND
social impact