5,594 research outputs found

    Classification of full exceptional collections of line bundles on three blow-ups of P3\mathbb{P}^{3}

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    A fullness conjecture of Kuznetsov says that if a smooth projective variety XX admits a full exceptional collection of line bundles of length ll, then any exceptional collection of line bundles of length ll is full. In this paper, we show that this conjecture holds for XX as the blow-up of P3\mathbb{P}^{3} at a point, a line, or a twisted cubic curve, i.e. any exceptional collection of line bundles of length 6 on XX is full. Moreover, we obtain an explicit classification of full exceptional collections of line bundles on such XX.Comment: 28 pages. To appear in Journal of the Korean Mathematical Society, A previous version with a different title appeared as [CGP17025] at https://cgp.ibs.re.kr/archive/preprints/201

    Genus-gg, nn-point, bb-boundary, cc-crosscap correlation functions of two-dimensional conformal field theory: Definition and general properties

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    We propose a systematic definition of genus-gg, nn-point, bb-boundary, cc-crosscap correlation functions Fg,n,b,cx\mathcal{F}_{g,n,b,c}^{x} with xx boundary operators, for general two-dimensional conformal field theory. The Fg,n,b,cx\mathcal{F}_{g,n,b,c}^{x} are defined as the inner products of the surface states with the tensor product of nn asymptotic states, bb boundary states and cc crosscap states, where the bb defining boundary states carry a total of xx boundary operators. The definition implies that Fg,n,b,cx\mathcal{F}_{g,n,b,c}^{x} are infinite linear combinations of genus-gg, (n+b+c)(n+b+c)-point functions Fg,(n+b+c)\mathcal{F}_{g,(n+b+c)}. A single pole structure is identified in the expansion coefficients Fg,n,b,c0\mathcal{F}_{g,n,b,c}^{0}, which is analogous to the single pole structure in the conformal block decomposition. This linear property unifies boundary and bulk CFTs. The consistency conditions of Fg,n,b,cx\mathcal{F}_{g,n,b,c}^{x} are discussed: conventional upper-half plane (UHP) and crosscap constraints can be reformulated as extra constraints on a collection of bulk correlation functions.Comment: 41 pages + references (Minor corrections + references added comparing to v1
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