Ramification Divisors of General Projections

  • Anand Deopurkar

    Mathematical Sciences Institute, Australian National University, Acton, ACT, Australia
  • Eduard Duryev

    Institute de Mathematiques de Jussieu, Paris, France
  • Anand Patel

    Department of Mathematics, Oklahoma State University, Stillwater, OK, USA
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We study ramification divisors of projections of a smooth projective variety onto a linear space of the same dimension. We prove that for a large class of varieties, the ramification divisors of such projections vary in a maximal dimensional family. We study the map that associates to a linear projection its ramification divisor. By a degeneration argument involving (linked) limit linear series of higher rank, we show that this map is dominant for most (but not all!) varieties of minimal degree.

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Anand Deopurkar, Eduard Duryev, Anand Patel, Ramification Divisors of General Projections. Doc. Math. 25 (2020), pp. 1917–1952

DOI 10.4171/DM/789