Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THE DIMENSION OF THE SPACE OF STABLE MAPS TO THE RELATIVE LAGRANGIAN GRASSMANNIAN OVER A CURVE

  • Received : 2023.01.09
  • Accepted : 2023.01.26
  • Published : 2023.02.28
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Abstract

Let C be a smooth projective curve and W a symplectic bundle over C of degree w. Let π : 𝕃𝔾(W) → C be the relative Lagrangian Grassmannian over C and Sd(W) be the space of Lagrangian subbundles of degree w -d. Then Kontsevich's space ${\bar{\mathcal{M}}}_g$(𝕃𝔾(W), βd) of stable maps to 𝕃𝔾(W) is a compactification of Sd(W). In this article, we give an upper bound on the dimension of ${\bar{\mathcal{M}}}_g$(𝕃𝔾(W), βd), which is an analogue of a result in [8] for the relative Lagrangian Grassmannian.

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Acknowledgement

This work was supported by Basic Science Research Programs through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2021R1I1A3049181).

References

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