Stability condition on Calabi-Yau threefold of complete intersection of quadratic and quartic hypersurfaces

Abstract

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 $X_{2,4}$. Applying the scheme proposed by Bayer, Bertram, Macrì, Stellari and Toda, we can construct an open subset of Bridgeland stability conditions on $X_{2,4}$.

arXiv commentChange the structure of the paper to make it more readable. No mathematical changes. Correct typos. Update reference. Update introduction. Prejournal version. To be published on Forum of Mathematics, Sigma. 33 pages, 3 figures, comments are very welcome! arXiv admin note: text overlap with arXiv:1810.03434 by other authors

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