<tt>diffstrata</tt>—A Sage Package for Calculations in the Tautological Ring of the Moduli Space of Abelian Differentials

Costantini, Matteo; Möller, Martin; Zachhuber, Jonathan

doi:10.1080/10586458.2021.1980750

Cited by 5 publications

(14 citation statements)

References 12 publications

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“…Deciding nonemptiness is the same as the realisability question that was addressed in [MUW21] purely in terms of graphs. The general version, taking into account the residue conditions, is stated in the algorithmic part of [CMZ20]. Note that these boundary strata may also be disconnected; see the discussion of prong-matching equivalence classes below.…”

Section: The Moduli Space Of Multi-scale Differentialsmentioning

confidence: 99%

The Chern classes and Euler characteristic of the moduli spaces of Abelian differentials

Costantini

Möller

Zachhuber

2022

Forum of Mathematics, Pi

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For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth compactification by multi-scale differentials. It is a consequence of a formula for the full Chern polynomial of the cotangent bundle of the compactification. The main new technical tools are an Euler sequence for the cotangent bundle of the moduli space of multi-scale differentials and computational tools in the Chow ring, such as a description of normal bundles to boundary divisors.

show abstract

Section: The Moduli Space Of Multi-scale Differentialsmentioning

confidence: 99%

The Chern classes and Euler characteristic of the moduli spaces of Abelian differentials

Costantini

Möller

Zachhuber

2022

Forum of Mathematics, Pi

Self Cite

View full text Add to dashboard Cite

show abstract

“…Deciding non-emptyness is the same as the realizability question that was addressed in [MUW17] purely in terms of graphs. The general version taking into account the residue conditions is stated in the algorithmic part of [CMZ20]. Note that these boundary strata may also be non-connected, see the discussion of prong-matching equivalence classes below.…”

Section: Theorem 31 ([Bcggm3]mentioning

confidence: 99%

“…This differs from the global residue condition in [BCGGM1] only in the subdivision of cases in i) and ii). As for the normal GRC (see [MUW17]),the R-GRC also has an algorithmic graph theoretic description, see [CMZ20].…”

Section: Clutching and Projection To Generalized Stratamentioning

confidence: 99%

“…Evaluation of top ξ-powers. First of all we explain how to evaluate the expression in Theoreom 1.3, see [CMZ20] for many algorithmic details. We only need to explain how to evaluate B ξ d , i.e.…”

Section: Examples: Geometry and Valuesmentioning

confidence: 99%

“…Specifically, the evaluation of tautological classes below is performed using the formula for fundamental classes of strata conjectured in [FP18] and [Sch18] and proven recently in [BHPSS20] based on results from [HS19]. The algorithms in this package are explained in [CMZ20].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials

Costantini¹,

Möller²,

Zachhuber³

2020

Preprint

Self Cite

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For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth compactification by multi-scale differentials. It is a consequence of a formula for the full Chern polynomial of the cotangent bundle of the compactification.The main new technical tools are an Euler sequence for the cotangent bundle of the moduli space of Abelian differentials and computational tools in the Chow ring, such as normal bundles to boundary divisors.

show abstract

`diffstrata`—A Sage Package for Calculations in the Tautological Ring of the Moduli Space of Abelian Differentials

Costantini

Möller

Zachhuber

2021

Experimental Mathematics

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`diffstrata`—A Sage Package for Calculations in the Tautological Ring of the Moduli Space of Abelian Differentials

Cited by 5 publications

References 12 publications

The Chern classes and Euler characteristic of the moduli spaces of Abelian differentials

The Chern classes and Euler characteristic of the moduli spaces of Abelian differentials

The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials

`diffstrata`—A Sage Package for Calculations in the Tautological Ring of the Moduli Space of Abelian Differentials

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diffstrata—A Sage Package for Calculations in the Tautological Ring of the Moduli Space of Abelian Differentials

Cited by 5 publications

References 12 publications

The Chern classes and Euler characteristic of the moduli spaces of Abelian differentials

The Chern classes and Euler characteristic of the moduli spaces of Abelian differentials

The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials

diffstrata—A Sage Package for Calculations in the Tautological Ring of the Moduli Space of Abelian Differentials

Contact Info

Product

Resources

About

`diffstrata`—A Sage Package for Calculations in the Tautological Ring of the Moduli Space of Abelian Differentials

`diffstrata`—A Sage Package for Calculations in the Tautological Ring of the Moduli Space of Abelian Differentials