@Article{         D2013,
  Author        = "D'Andrea, Carlos and Krick, Teresa and Sombra, Mart{\'\i}n",
  Abstract      = "We present bounds for the degree and the height of the polynomials arising in some problems in effective algebraic geometry including the implicitization of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A key role is played by the notion of canonical mixed height of a multiprojective variety. We study this notion from the point of view of resultant theory and establish some of its basic properties, including its behavior with respect to intersections, projections and products. We obtain analogous results for the function field case, including a parametric Nullstellensatz.",
  date-added    = "2022-11-26 17:23:09 +0100",
  date-modified = "2022-11-28 09:05:51 +0100",
  Journal       = "Annales scientifiques de l'{\'E}cole Normale Sup{\'e}rieure",
  Keywords      = "multiprojective spaces; mixed heights; resultants; implicitization; arithmetic nullstellensatz",
  Language      = "eng",
  Number        = "4",
  Pages         = "549-627",
  Publisher     = "Soci{\'e}t{\'e} math{\'e}matique de France",
  Title         = {Heights of varieties in multiprojective spaces and arithmetic Nullstellens{\"a}tze},
  URL           = "http://eudml.org/doc/272167",
  Volume        = "46",
  Year          = "2013",
  bdsk-url-1    = "http://eudml.org/doc/272167",
  File          = "Heights of varieties in multiprojective spaces and arithmetic Nullstellensätze - ASENS\_2013\_4\_46\_4\_549\_0 - a.pdf"
}

@Article{ D2013, Author = "D'Andrea, Carlos and Krick, Teresa and Sombra, Mart{\'\i}n", Abstract = "We present bounds for the degree and the height of the polynomials arising in some problems in effective algebraic geometry including the implicitization of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A key role is played by the notion of canonical mixed height of a multiprojective variety. We study this notion from the point of view of resultant theory and establish some of its basic properties, including its behavior with respect to intersections, projections and products. We obtain analogous results for the function field case, including a parametric Nullstellensatz.", date-added = "2022-11-26 17:23:09 +0100", date-modified = "2022-11-28 09:05:51 +0100", Journal = "Annales scientifiques de l'{\'E}cole Normale Sup{\'e}rieure", Keywords = "multiprojective spaces; mixed heights; resultants; implicitization; arithmetic nullstellensatz", Language = "eng", Number = "4", Pages = "549-627", Publisher = "Soci{\'e}t{\'e} math{\'e}matique de France", Title = {Heights of varieties in multiprojective spaces and arithmetic Nullstellens{\"a}tze}, URL = "http://eudml.org/doc/272167", Volume = "46", Year = "2013", bdsk-url-1 = "http://eudml.org/doc/272167", File = "Heights of varieties in multiprojective spaces and arithmetic Nullstellensätze - ASENS_2013_4_46_4_549_0 - a.pdf" }