Del Pezzo elliptic varieties of degree d <= 4

Luca Ugaglia, Andrea L. Tironi, Antonio Laface

Risultato della ricerca: Article

Abstract

Let Y be a smooth del Pezzo variety of dimension n&gt;=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 &gt;= 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 -&gt; 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 originaleEnglish
pagine (da-a)1085-1110
Numero di pagine26
RivistaANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE
Volume19
Stato di pubblicazionePublished - 2019

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

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