# Jacobian rings for homogenous vector bundles and applications

@article{Huang2018JacobianRF, title={Jacobian rings for homogenous vector bundles and applications}, author={An Huang and Bong H. Lian and Shing-Tung Yau and Chenglong Yu}, journal={arXiv: Algebraic Geometry}, year={2018} }

In this note, we examine the Jacobian ring description of the Hodge structure of zero loci of vector bundle sections on a class of ambient varieties. We consider a set of cohomological vanishing conditions that imply such a description, and we verify these conditions for some new cases. We also observe that the method can be directly extended to log homogeneous varieties. We apply the Jacobian ring to study the null varieties of period integrals and their derivatives, generalizing a result in…

## 3 Citations

Picard-Fuchs Systems Arising From Toric and Flag Varieties

- Mathematics
- 2018

This thesis studies the Picard-Fuchs systems for families arising as vector bundles zero loci in toric or partial flag varieties, including Riemann-Hilbert type theorems and arithmetic properties of…

Hochschild cohomology of generalised Grassmannians

- Mathematics
- 2019

We compute the Hochschild-Kostant-Rosenberg decomposition of the Hochschild cohomology of generalised Grassmannians, i.e. partial flag varieties associated to maximal parabolic subgroups in a simple…

A note on a Griffiths-type ring for complete intersections in Grassmannians

- Mathematics, Geology
- 2018

We calculate a Griffiths-type ring for smooth complete intersection in Grassmannians. This is the analogue of the classical Jacobian ring for complete intersections in projective space, and allows us…

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