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• W2963403028 abstract "Let<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X><mml:semantics><mml:mi>X</mml:mi><mml:annotation encoding=application/x-tex>X</mml:annotation></mml:semantics></mml:math></inline-formula>be a smooth projective variety over the complex numbers, and let<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper D subset-of upper X><mml:semantics><mml:mrow><mml:mi>D</mml:mi><mml:mo>⊂<!-- ⊂ --></mml:mo><mml:mi>X</mml:mi></mml:mrow><mml:annotation encoding=application/x-tex>Dsubset X</mml:annotation></mml:semantics></mml:math></inline-formula>be an ample divisor. For which spaces<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Y><mml:semantics><mml:mi>Y</mml:mi><mml:annotation encoding=application/x-tex>Y</mml:annotation></mml:semantics></mml:math></inline-formula>is the restriction map<disp-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=r colon normal upper H normal o normal m left-parenthesis upper X comma upper Y right-parenthesis right-arrow normal upper H normal o normal m left-parenthesis upper D comma upper Y right-parenthesis><mml:semantics><mml:mrow><mml:mi>r</mml:mi><mml:mo>:</mml:mo><mml:mrow class=MJX-TeXAtom-ORD><mml:mi mathvariant=normal>H</mml:mi><mml:mi mathvariant=normal>o</mml:mi><mml:mi mathvariant=normal>m</mml:mi></mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>Y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo stretchy=false>→<!-- → --></mml:mo><mml:mrow class=MJX-TeXAtom-ORD><mml:mi mathvariant=normal>H</mml:mi><mml:mi mathvariant=normal>o</mml:mi><mml:mi mathvariant=normal>m</mml:mi></mml:mrow><mml:mo stretchy=false>(</mml:mo><mml:mi>D</mml:mi><mml:mo>,</mml:mo><mml:mi>Y</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>begin{equation*}r: mathrm {Hom}(X, Y)to mathrm {Hom}(D, Y) end{equation*}</mml:annotation></mml:semantics></mml:math></disp-formula>an isomorphism? Using positive characteristic methods, we give a fairly exhaustive answer to this question. An example application of our techniques is: if<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=dimension left-parenthesis upper X right-parenthesis greater-than-or-equal-to 3><mml:semantics><mml:mrow><mml:mi>dim</mml:mi><mml:mo>⁡<!-- ⁡ --></mml:mo><mml:mo stretchy=false>(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>≥<!-- ≥ --></mml:mo><mml:mn>3</mml:mn></mml:mrow><mml:annotation encoding=application/x-tex>dim (X)geq 3</mml:annotation></mml:semantics></mml:math></inline-formula>,<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Y><mml:semantics><mml:mi>Y</mml:mi><mml:annotation encoding=application/x-tex>Y</mml:annotation></mml:semantics></mml:math></inline-formula>is smooth,<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Omega Subscript upper Y Superscript 1><mml:semantics><mml:msubsup><mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi><mml:mi>Y</mml:mi><mml:mn>1</mml:mn></mml:msubsup><mml:annotation encoding=application/x-tex>Omega ^1_Y</mml:annotation></mml:semantics></mml:math></inline-formula>is nef, and<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=dimension left-parenthesis upper Y right-parenthesis greater-than dimension left-parenthesis upper D right-parenthesis comma><mml:semantics><mml:mrow><mml:mi>dim</mml:mi><mml:mo>⁡<!-- ⁡ --></mml:mo><mml:mo stretchy=false>(</mml:mo><mml:mi>Y</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>></mml:mo><mml:mi>dim</mml:mi><mml:mo>⁡<!-- ⁡ --></mml:mo><mml:mo stretchy=false>(</mml:mo><mml:mi>D</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>,</mml:mo></mml:mrow><mml:annotation encoding=application/x-tex>dim (Y)> dim (D),</mml:annotation></mml:semantics></mml:math></inline-formula>the restriction map<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=r><mml:semantics><mml:mi>r</mml:mi><mml:annotation encoding=application/x-tex>r</mml:annotation></mml:semantics></mml:math></inline-formula>is an isomorphism. Taking<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Y><mml:semantics><mml:mi>Y</mml:mi><mml:annotation encoding=application/x-tex>Y</mml:annotation></mml:semantics></mml:math></inline-formula>to be the classifying space of a finite group<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper B upper G><mml:semantics><mml:mrow><mml:mi>B</mml:mi><mml:mi>G</mml:mi></mml:mrow><mml:annotation encoding=application/x-tex>BG</mml:annotation></mml:semantics></mml:math></inline-formula>, the moduli space of pointed curves<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper M Subscript g comma n><mml:semantics><mml:msub><mml:mrow class=MJX-TeXAtom-ORD><mml:mi mathvariant=script>M</mml:mi></mml:mrow><mml:mrow class=MJX-TeXAtom-ORD><mml:mi>g</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:annotation encoding=application/x-tex>mathscr {M}_{g,n}</mml:annotation></mml:semantics></mml:math></inline-formula>, the moduli space of principally polarized Abelian varieties<inline-formula content-type=math/mathml><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper A Subscript g><mml:semantics><mml:msub><mml:mrow class=MJX-TeXAtom-ORD><mml:mi mathvariant=script>A</mml:mi></mml:mrow><mml:mi>g</mml:mi></mml:msub><mml:annotation encoding=application/x-tex>mathscr {A}_g</mml:annotation></mml:semantics></mml:math></inline-formula>, certain period domains, and various other moduli spaces, one obtains many new and classical Lefschetz hyperplane theorems." @default.
• W2963403028 created "2019-07-30" @default.
• W2963403028 creator A5013284360 @default.
• W2963403028 date "2018-05-17" @default.
• W2963403028 modified "2023-09-23" @default.
• W2963403028 title "Non-Abelian Lefschetz hyperplane theorems" @default.
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• W2963403028 doi "https://doi.org/10.1090/jag/704" @default.
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