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Gamma conjecture I for blowing up $\mathbb{P}^n$ along $\mathbb{P}^r$

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arxiv 2202.04234 v1 pith:MKTRK2NB submitted 2022-02-09 math.AG

classification math.AG
keywords mathbbconjecturealongblowinggammacheckconditionsconifold
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abstract

Consider the Fano manifold $X$ formed by blowing up $\mathbb{P}^n$ along its linear subspace $\mathbb{P}^r$, we check the conifold conditions [3, 1] for its mirror Laurent polynomial $f$, which can imply that $X$ satisfies both Conjecture $\mathcal{O}$ and Gamma conjecture I by Galkin-Golyshev-Iritani [2].

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