2018
DOI: 10.48550/arxiv.1804.09544
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Blow ups of $\mathbb{P^n}$ as quiver moduli for exceptional collections

Xuqiang Qin

Abstract: Suppose P n m is the blow up of P n at a linear subspace of dimension m, L = {L 1 , . . . , Lr} is a (not necessarily full) strong exceptional collection of line bundles on P n m . Let Q be the quiver associated to this collection. One might wonder when is P n m the moduli space of representations of Q with dimension vector (1, . . . , 1) for a suitably chosen stability condition θ: S ∼ = M θ . In this paper, we achieve such isomorphism using L of length 3. As a result, P n m is the moduli space of representat… Show more

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Cited by 2 publications
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“…Therefore, the geometry of C(Q) describes the birational geometry of these compactifications. Particular examples of algebraic varieties constructed via our package include the blow up of P n along a linear subspace, see [Qin18], and toric compactifications of the moduli space of n labeled points in P 1 , see [BH20].…”
Section: Applications To Moduli Spacesmentioning
confidence: 99%
“…Therefore, the geometry of C(Q) describes the birational geometry of these compactifications. Particular examples of algebraic varieties constructed via our package include the blow up of P n along a linear subspace, see [Qin18], and toric compactifications of the moduli space of n labeled points in P 1 , see [BH20].…”
Section: Applications To Moduli Spacesmentioning
confidence: 99%
“…The curious readers are referred to the extended version of the present paper [20]. The techniques also apply to some varieties in higher dimension, see [19].…”
Section: Introductionmentioning
confidence: 99%