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<p>Given a smooth, open, oriented surface <i>X</i> endowed with a family of complex structures <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\{J_b\}_{b\in B}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mo stretchy="false">{</mo> <msub> <mi>J</mi> <mi>b</mi> </msub> <mo stretchy="false">}</mo> </mrow> <mrow> <mi>b</mi> <mo>∈</mo> <mi>B</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> depending continuously on the parameter <i>b</i> in a metrisable space <i>B</i>, we construct a continuous family of proper holomorphic maps <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(F_{b}:(X,J_b)\rightarrow \mathbb {C}^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>F</mi> <mi>b</mi> </msub> <mo>:</mo> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <msub> <mi>J</mi> <mi>b</mi> </msub> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">→</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(b\in B\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>b</mi> <mo>∈</mo> <mi>B</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Families of proper holomorphic maps

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月2日

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  • Barbara Drinovec Drnovšek,
  • Jure Kališnik

摘要

Given a smooth, open, oriented surface X endowed with a family of complex structures \(\{J_b\}_{b\in B}\) { J b } b ∈ B depending continuously on the parameter b in a metrisable space B, we construct a continuous family of proper holomorphic maps \(F_{b}:(X,J_b)\rightarrow \mathbb {C}^{2}\) F b : ( X , J b ) → C 2 , \(b\in B\) b ∈ B .