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Abstract We prove that the nonvarying strata of abelian and quadratic differentials in low genus have trivial tautological rings and are affine varieties. We also prove that strata ofk-differentials of infinite area are affine varieties for allk. Vanishing of homology in degree higher than the complex dimension follows as a consequence for these affine strata. Moreover we prove that the stratification of the Hodge bundle for abelian and quadratic differentials of finite area is extremal in the sense that merging two zeros in each stratum leads to an extremal effective divisor in the boundary. A common feature throughout these results is a relation of divisor classes in strata of differentials as well as its incarnation in Teichmüller dynamics.
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This content will become publicly available on March 19, 2026
Filtration and splitting of the Hodge bundle on the nonvarying strata of quadratic differentials
We describe the Harder–Narasimhan filtration of the Hodge bundle for Teichmüller curves in the nonvarying strata of quadratic differentials appearing in the work of Dawei Chen and Martin Möller [Ann. Sci. ’Ec. Norm. Sup’er. (4) 47 (2014), pp. 309–369]. Moreover, we show that the Hodge bundle on the nonvarying strata away from the irregular components can split as a direct sum of line bundles. As applications, we determine all individual Lyapunov exponents of algebraically primitive Teichmüller curves in the nonvarying strata and derive new results regarding the asymptotic behavior of Lyapunov exponents.
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- Award ID(s):
- 2301030
- PAR ID:
- 10591657
- Publisher / Repository:
- Transactions of the American Mathematical Society
- Date Published:
- Journal Name:
- Transactions of the American Mathematical Society
- ISSN:
- 0002-9947
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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