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• W1809304315 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L> <mml:semantics> <mml:mi>L</mml:mi> <mml:annotation encoding=application/x-tex>L</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be an ample line bundle over a complex abelian variety <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that the space of all global sections over <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper D i f f Subscript upper A Superscript n Baseline left-parenthesis upper L comma upper L right-parenthesis> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>Diff</mml:mi> <mml:mi>A</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi>L</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>operatorname {Diff}^{n}_A(L,L)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper S Superscript n Baseline left-parenthesis upper D i f f Subscript upper A Superscript 1 Baseline left-parenthesis upper L comma upper L right-parenthesis right-parenthesis> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>S</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:msubsup> <mml:mi>Diff</mml:mi> <mml:mi>A</mml:mi> <mml:mn>1</mml:mn> </mml:msubsup> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi>L</mml:mi> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>S^n(operatorname {Diff}^1_A(L,L))</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are both of dimension one. Using this it is shown that the moduli space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M Subscript upper X> <mml:semantics> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>X</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>M_X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of rank one holomorphic connections on a compact Riemann surface <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> does not admit any nonconstant algebraic function. On the other hand, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M Subscript upper X> <mml:semantics> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>X</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>M_X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is biholomorphic to the moduli space of characters of <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>, which is an affine variety. So <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M Subscript upper X> <mml:semantics> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>X</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>M_X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is algebraically distinct from the character variety if <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> is of genus at least one." @default.
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• W1809304315 date "2002-06-04" @default.
• W1809304315 modified "2023-10-18" @default.
• W1809304315 title "Differential operators on a polarized abelian variety" @default.
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