It is known that properly elliptic surfaces S \subset P^n of degree d and class m satisfy the inequality m-3d \geq 2, equality implying that S is minimal, \chi(O_S)=0 and the base curve of the elliptic fibration is rational. Using the progress in understanding such surfaces made by Serrano, the result above is improved considerably. In fact it turns out that for S as above m-3d \geq 6, equality implying that S is an elliptic quasi-bundle over a smooth curve C of genus 0 or 1 and in both cases p_g, q and the multiplicities of the multiple fibers are determined. The result is effective and applies to describe smooth projective surfaces S \subset P^n satisfying the condition m \leq 3d+6.

On the class of an elliptic projective surface / A. Lanteri. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - 64:4(1995), pp. 359-368.

### On the class of an elliptic projective surface

#### Abstract

It is known that properly elliptic surfaces S \subset P^n of degree d and class m satisfy the inequality m-3d \geq 2, equality implying that S is minimal, \chi(O_S)=0 and the base curve of the elliptic fibration is rational. Using the progress in understanding such surfaces made by Serrano, the result above is improved considerably. In fact it turns out that for S as above m-3d \geq 6, equality implying that S is an elliptic quasi-bundle over a smooth curve C of genus 0 or 1 and in both cases p_g, q and the multiplicities of the multiple fibers are determined. The result is effective and applies to describe smooth projective surfaces S \subset P^n satisfying the condition m \leq 3d+6.
##### Scheda breve Scheda completa Scheda completa (DC)
projective surface; projective character; elliptic surface; ellip[tic quasi-bundle; very ample divisor
Settore MAT/03 - Geometria
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
##### Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

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/2434/188083
• ND
• 6
• 5