Abstract
Let Y be a smooth del Pezzo variety of dimension n>=3, i.e. a smooth complex projective variety endowed with an ample divisor H such that K_Y = (n+1)H. Let d be the degree H^n of Y and assume that d >= 4. Consider a linear subsystem of |H| whose base locus is zero-dimensional of length d. The subsystem defines a rational map onto P^{n-1} and, under some mild extra hypothesis, the general pseudofibers are elliptic curves. We study the elliptic fibration X -> P^{n-1} obtained by resolving the indeterminacy and call the variety X a del Pezzo elliptic variety. Extending the results of [7] we mainly prove that the Mordell-Weil group of the fibration is finite if and only if the Cox ring of X is finitely generated.
Lingua originale | English |
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pagine (da-a) | 1085-1110 |
Numero di pagine | 26 |
Rivista | ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE |
Volume | 19 |
Stato di pubblicazione | Published - 2019 |
All Science Journal Classification (ASJC) codes
- ???subjectarea.asjc.2600.2614???
- ???subjectarea.asjc.2600.2601???