Two-dimensional families of hyperelliptic jacobians with big monodromy

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Abstract

Let K be a global field of characteristic different from 2 and u(x) ∈ K[x] be an irreducible polynomial of even degree 2g ≥ 6 whose Galois group over K is either the full symmetric group (formula presented) or the alternating group A2g. We describe explicitly how to choose (infinitely many) pairs of distinct t1, t2∈ K such that the g-dimensional Jacobian of a hyperelliptic curve y2= (x−t1)(x−t2))u(x) has no nontrivial endomorphisms over an algebraic closure of K and has big monodromy.

Original languageEnglish (US)
Pages (from-to)3651-3672
Number of pages22
JournalTransactions of the American Mathematical Society
Volume368
Issue number5
DOIs
StatePublished - May 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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