The Hodge number \(h^{1,1}\) of irregular algebraic surfaces

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• 作者：Andrea Causin ; Margarida Mendes Lopes ; Gian Pietro Pirola
• 关键词：Primary 14J29 ; Secondary 14C30 ; 15A30 ; 32J25
• 刊名：Collectanea Mathematica
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：67
• 期：1
• 页码：63-68
• 全文大小：380 KB
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• 作者单位：Andrea Causin (1)
  Margarida Mendes Lopes (2)
  Gian Pietro Pirola (3)
  
  1. D.A.D.U., Università di Sassari, Piazza Duomo 6, 07041, Alghero, SS, Italy
  2. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal
  3. Dipartimento di Matematica, Università di Pavia, Via Ferrata, 1, 27100, Pavia, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  Analysis
  Applications of Mathematics
  Geometry
  
• 出版者：Springer Milan
• ISSN：2038-4815

文摘

We prove a new inequality for the Hodge number \(h^{1,1}\) of irregular complex smooth projective surfaces of general type without irrational pencils of genus \(\ge \)2. More specifically we show that if the irregularity \(q\) satisfies \(q=2^k+1\) then \(h^{1,1}\ge 4q-3\). This generalizes results previously known for \(q=3\) and \(q=5\). Mathematics Subject Classification Primary 14J29 Secondary 14C30 15A30 32J25