Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class

Bisogno, Dean; Li, Wanlin; Litt, Daniel; Srinivasan, Padmavathi

doi:10.48550/arxiv.2004.06146

Cited by 1 publication

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“…and it is readily checked that A 2 (0) (C 2 ) injects into cohomology. This argument also applies to the second relation of (7).…”

Section: The Main Resultsmentioning

confidence: 85%

“…The relations (7) are pullbacks of relations taking place in R * (C 2 ). The first relation of ( 7) concerns the Faber-Pandharipande cycle of Remark 2.14.…”

Section: The Main Resultsmentioning

confidence: 99%

“…Theorem 3.1 provides the first examples of non-hyperelliptic curves with an MCK decomposition. These are also the first examples of non-hyperelliptic curves with torsion Ceresa cycle (non-hyperelliptic examples where the class of the Ceresa cycle in the intermediate Jacobian is torsion are given in [7] and [4], cf. also [5] for a result modulo algebraic equivalence 1 ).…”

Section: Introductionmentioning

confidence: 89%

“…Remark 4.3. In [7] and [5], examples are given of non-hyperelliptic curves for which the Ceresa cycle is torsion modulo algebraic equivalence. In view of [16,Remark 3.4], these curves hence have an MCK decomposition modulo algebraic equivalence (and the argument of Theorem 3.2 gives that the tautological ring modulo algebraic equivalence of these curves injects into cohomology).…”

Section: Closing Remarksmentioning

confidence: 99%

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On the tautological ring of Humbert curves

Laterveer

2022

manuscripta math.

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We exhibit a 2-dimensional family of non-hyperelliptic curves of genus 5, called Humbert curves, for which the tautological ring injects into cohomology. In particular, Humbert curves have a multiplicative Chow-Künneth decomposition (in the sense of Shen-Vial), and their Ceresa cycle is torsion.Theorem (=Theorems 3.1 and 3.2). Let C be a Humbert curve, and m ∈ N. Letgenerated by (pullbacks of) the diagonal ∆ C ⊂ C × C and (pullbacks of) the canonical divisor K C . The cycle class map induces injections R * (C m ) ֒→ H * (C m , Q) for all m ∈ N.

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“…and it is readily checked that A 2 (0) (C 2 ) injects into cohomology. This argument also applies to the second relation of (7).…”

Section: The Main Resultsmentioning

confidence: 85%

“…The relations (7) are pullbacks of relations taking place in R * (C 2 ). The first relation of ( 7) concerns the Faber-Pandharipande cycle of Remark 2.14.…”

Section: The Main Resultsmentioning

confidence: 99%