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- W2092731650 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper H normal i normal l normal b Superscript g Baseline upper S> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>H</mml:mi> <mml:mi mathvariant=normal>i</mml:mi> <mml:mi mathvariant=normal>l</mml:mi> <mml:mi mathvariant=normal>b</mml:mi> </mml:mrow> <mml:mi>g</mml:mi> </mml:msup> <mml:mi>S</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathrm {Hilb}^gS</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the Hilbert scheme of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=g> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding=application/x-tex>g</mml:annotation> </mml:semantics> </mml:math> </inline-formula> points on a K3 surface <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper S> <mml:semantics> <mml:mi>S</mml:mi> <mml:annotation encoding=application/x-tex>S</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Suppose that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper P normal i normal c upper S approximately-equals double-struck upper Z upper C> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>P</mml:mi> <mml:mi mathvariant=normal>i</mml:mi> <mml:mi mathvariant=normal>c</mml:mi> </mml:mrow> <mml:mi>S</mml:mi> <mml:mo>≅<!-- ≅ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>Z</mml:mi> </mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathrm {Pic}Scong mathbb {Z}C</mml:annotation> </mml:semantics> </mml:math> </inline-formula> where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C> <mml:semantics> <mml:mi>C</mml:mi> <mml:annotation encoding=application/x-tex>C</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a smooth curve with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C squared equals 2 left-parenthesis g minus 1 right-parenthesis n squared> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>C</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy=false>(</mml:mo> <mml:mi>g</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>C^2=2(g-1)n^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We prove that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper H normal i normal l normal b Superscript g Baseline upper S> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>H</mml:mi> <mml:mi mathvariant=normal>i</mml:mi> <mml:mi mathvariant=normal>l</mml:mi> <mml:mi mathvariant=normal>b</mml:mi> </mml:mrow> <mml:mi>g</mml:mi> </mml:msup> <mml:mi>S</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathrm {Hilb}^gS</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a Lagrangian fibration." @default.
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- W2092731650 date "2006-12-06" @default.
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- W2092731650 title "Lagrangian fibrations on Hilbert schemes of points on K3 surfaces" @default.
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