Non abelian theta functions and the theta map

Arnaud Beauville

Description

Non-abelian theta functions and the theta map Arnaud Beauville Universite de Nice Berkeley, April 2009 Arnaud Beauville Non-abelian theta functions and the theta map

• poles ≤


• abelian theta


• theta functions


• bundles


• riemann surface


• functions


• complex torus


• universite de nice


• line bundles trivial


• line bundles

Sujets

• Beauville
• Theta function
• Bundle
• Riemann surface
• Function
• Complex torus
• Universidad de Niza Sophia Antipolis

Informations

• Publié par: pefav
• Nombre de lectures: 23
• Langue: English

Extrait

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Berkeley, April 2009

Non-abelian

theta functions and

the

theta

map

Arnaud Beauville

Universit´edeNice

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Non-abelian

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Arnaud

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Θ := { L ∈ J | H 0 ( L ) 6 = 0 }

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C curve (= Riemann surface) of genus g . Topologically, line bundles on C are classified by the degree deg L ∈ Z .

J d := { isom. classes of line bundles of degree d on C } = ∼ J 0 = the Jacobian of C = ∼ complex torus C g / Γ

We will focus on J := J g − 1 .

hypersurface in J ( theta divisor ) .

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Abelian theta functions C curve (= Riemann surface) of genus g . Topologically, line bundles on C are classified by the degree deg L ∈ Z . J d := { isom. classes of line bundles of degree d on C } ∼ = J 0 = the Jacobian of C ∼ = complex torus C g / Γ We will focus on J := J g − 1 . Θ := { L ∈ J | H 0 ( L ) 6 = 0 } hypersurface in J ( theta divisor ) . Definition { theta functions of order k } := H 0 ( J  O J ( k Θ)) Arnaud Beauville Non-abelian theta functions and the theta map

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= { meromorphic functions on J with poles ≤ k Θ } ;

Definition { theta functions of order k } := H 0 ( J  O J ( k Θ))

Θ := { L ∈ J | H 0 ( L ) 6 = 0 } hypersurface in J ( theta divisor ) .

We will focus on J := J g − 1 .

mate

C curve (= Riemann surface) of genus g . Topologically, line bundles on C are classified by the degree deg L ∈ Z . J d := { isom. classes of line bundles of degree d on C } = ∼ J 0 = the Jacobian of C = ∼ complex torus C g / Γ

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