Geodesic
Stability condition on Calabi–Yau threefold of complete intersection of quadratic and quartic hypersurfaces
Forum of Mathematics, Sigma, Tome 10 (2022)

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In this paper, we prove a Clifford type inequality for the curve $X_{2,2,2,4}$, which is the intersection of a quartic and three general quadratics in $\mathbb {P}^5$. We thus prove a stronger Bogomolov–Gieseker inequality for characters of stable vector bundles and stable objects on Calabi–Yau complete intersection $X_{2,4}$. Applying the scheme proposed by Bayer, Bertram, Macrì, Stellari and Toda, we can construct an open subset of Bridgeland stability conditions on $X_{2,4}$. 
@article{10_1017_fms_2022_96,
     author = {Shengxuan Liu},
     title = {Stability condition on {Calabi{\textendash}Yau} threefold of complete intersection of quadratic and quartic hypersurfaces},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {10},
     year = {2022},
     doi = {10.1017/fms.2022.96},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.96/}
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Shengxuan Liu. Stability condition on Calabi–Yau threefold of complete intersection of quadratic and quartic hypersurfaces. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.96

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