0000000000489808

AUTHOR

Stefan Reiter

showing 2 related works from this author

Some fourth order CY-type operators with non symplectically rigid monodromy

2012

We study tuples of matrices with rigidity index two in $\Sp_4(\mathbb{C})$, which are potentially induced by differential operators of Calabi-Yau type. The constructions of those monodromy tuples via algebraic operations and middle convolutions and the related constructions on the level differential operators lead to previously known and new examples.

Pure mathematicsGeneral Mathematics010102 general mathematics010103 numerical & computational mathematicsDifferential operator01 natural sciencesMathematics - Algebraic GeometryFourth orderMathematics::Algebraic GeometryMonodromyMathematics - Classical Analysis and ODEsAlgebraic operationClassical Analysis and ODEs (math.CA)FOS: MathematicsHadamard product0101 mathematicsTupleMathematics::Symplectic GeometryAlgebraic Geometry (math.AG)Mathematics
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On symplectically rigid local systems of rank four and Calabi–Yau operators

2013

AbstractWe classify all Sp4(C)-rigid, quasi-unipotent local systems and show that all of them have geometric origin. Furthermore, we investigate which of those having a maximal unipotent element are induced by fourth order Calabi–Yau operators. Via this approach, we reconstruct all known Calabi–Yau operators inducing an Sp4(C)-rigid monodromy tuple and obtain closed formulae for special solutions of them.

Pure mathematicsAlgebra and Number TheoryHadamard productRank (linear algebra)Geometric originUnipotentOperator theoryConvolutionConvolutionAlgebraComputational MathematicsMathematics::Algebraic GeometryMonodromyRigidityCalabi–Yau operatorsCalabi–Yau manifoldHadamard productMathematics::Differential GeometryTupleMathematics::Symplectic GeometryMathematicsJournal of Symbolic Computation
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