2019
DOI: 10.1215/00127094-2019-0014
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Hori-mological projective duality

Abstract: Kuznetsov has conjectured that Pfaffian varieties should admit non-commutative crepant resolutions which satisfy his Homological Projective Duality. We prove half the cases of this conjecture, by interpreting and proving a duality of non-abelian gauged linear sigma models proposed by Hori. Contents 1. Introduction 1 1.1. The non-commutative resolutions 3 1.2. A sketch of the physics 6 1.3. A sketch of our proof 8 2. Technical background 2.1. Matrix factorization categories 2.2. Homological projective duality v… Show more

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Cited by 16 publications
(25 citation statements)
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“…If we choose a generic L, there is a noncommutative resolution B L of Pf q | L [17,18], and if Pf q | L is smooth D b (coh B L ) is equivalent to D b (coh Pf q | L ). Combining Theorem 1.2 and the results in [16], we have the following. and that Λ is a noncommutative resolution of the affine quotient W/ GSp(Q) of a certain representation W of the symplectic similitude group GSp(Q) of a symplectic vector space Q.…”
Section: Resultsmentioning
confidence: 59%
See 1 more Smart Citation
“…If we choose a generic L, there is a noncommutative resolution B L of Pf q | L [17,18], and if Pf q | L is smooth D b (coh B L ) is equivalent to D b (coh Pf q | L ). Combining Theorem 1.2 and the results in [16], we have the following. and that Λ is a noncommutative resolution of the affine quotient W/ GSp(Q) of a certain representation W of the symplectic similitude group GSp(Q) of a symplectic vector space Q.…”
Section: Resultsmentioning
confidence: 59%
“…More precisely, we prove that G-equivariant tilting modules over G-equivariant algebras induce equivalences of derived factorization categories of noncommutative gauged LG models. Moreover, combining Rennemo-Segal's results in [16] with our result, we prove that the derived category of a noncommutative resolution of a generic linear section of a Pfaffian variety is equivalent to the derived factorization category of a noncommutative gauged LG model (Λ, χ, w) Gm , where Λ is a non-commutative resolution of the quotient singularity W/ GSp(Q) arising from a certain representation W of the symplectic similitude group GSp(Q) of a symplectic vector space Q.…”
Section: Backgroundsmentioning
confidence: 75%
“…Despite these complications, it seems that D-brane transport and in particular monodromy calculations as advertised here also work in the non-abelian case [28,45]. See also [46][47][48] for recent work in mathematics in this context.…”
Section: Discussionmentioning
confidence: 99%
“…(A) In this case A is the complement of 108 exceptional objects in D b (Y ), while D b (Z) is generated by 32 exceptional objects by homological projective duality [30,Th. 4.33], since Z is isomorphic to a hyperplane section of Gr(2, 10) .…”
Section: Proposition 24mentioning
confidence: 99%
“…(B) In this case D b (Z 1 ) is generated by 22 exceptional objects, by (incomplete) homological projective duality [30,Th. 4.33], since it is isomorphic to a double hyperplane section of Gr(2, 9) and odd Pfaffians have codimension 3 so that the projective dual of Z 1 is empty.…”
Section: Proposition 24mentioning
confidence: 99%