On motivic vanishing cycles of critical loci

Bussi, Vittoria; Joyce, Dominic; Meinhardt, Sven

doi:10.48550/arxiv.1305.6428

Cited by 19 publications

(74 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Writing X an for the complex analytic topological space of X, the obstruction to existence of orientations for (X, ω * X ) lies in H 2 (X an ; Z 2 ), and if the obstruction vanishes, the set of orientations is a torsor for H 1 (X an ; Z 2 ). This notion of orientation, and its analogue for 'd-critical loci', are used by Ben-Bassat, Brav, Bussi, Dupont, Joyce, Meinhardt, and Szendrői in a series of papers [2][3][4][5]21]. They use orientations on (X, ω * X ) to define natural perverse sheaves, D-modules, mixed Hodge modules, and motives on X.…”

Section: Orientations On K-shifted Symplectic Derived Schemesmentioning

confidence: 99%

“…We prove Theorem 1.1 using a 'Darboux Theorem' for k-shifted symplectic derived schemes by Bussi, Brav and the second author [4]. This paper is related to the series [2][3][4][5]21], mostly concerning the −1-shifted (3-Calabi-Yau) case.…”

Section: Introductionmentioning

confidence: 98%

“…In §2. 5 we give a short definition of Kuranishi atlases K on a topological space X. These are families of 'Kuranishi neighbourhoods' (V, E, s, ψ) on X and 'coordinate changes' between them, based on work of Fukaya, Oh, Ohta and Ono [14,15] in symplectic geometry.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Virtual fundamental classes for moduli spaces of sheaves on Calabi–Yau four-folds

2017

Self Cite

View full text Add to dashboard Cite

It is shown that any derived scheme over C equipped with a´2-shifted symplectic structure, and having a Hausdorff space of classical points, admits a globally defined Lagrangian distribution as a dg C 8 -manifold. The main tool for proving this theorem is a strictification result for Lagrangian distribution. It is shown that existence of a global Lagrangian distribution allows us to realize the moduli space of sheaves on Calabi-Yau fourfolds as a derived critical locus of a potential of degree´1 on the moduli space of Spinp7q instantons.

show abstract

Section: Orientations On K-shifted Symplectic Derived Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Virtual fundamental classes for moduli spaces of sheaves on Calabi–Yau four-folds

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…Joyce etc. have a working group on the motivic DT-theory, see [14], [15]. It is interesting to see how motivic DT-invariants change under orbifold flops.…”

Section: Motivic Dt-invariants and Flopsmentioning

confidence: 99%

Donaldson–Thomas invariants of Calabi–Yau orbifolds under flops

Jiang¹

2018

Illinois J. Math.

View full text Add to dashboard Cite

We study the Donaldson-Thomas type invariants for the Calabi-Yau threefold Deligne-Mumford stacks under flops. A crepant birational morphism between two smooth Calabi-Yau threefold Deligne-Mumford stacks is called an orbifold flop if the flopping locus is the quotient of weighted projective lines by a cyclic group action. We prove that the Donaldson-Thomas invariants are preserved under orbifold flops. CONTENTSYUNFENG JIANG Proof of Theorem 1.3 32 6. Discussion on the Hard Lefschetz condition. 32 33 References 33 DONALDSON-THOMAS INVARIANTS UNDER FLOPS 3 Definition 1.1. ([43]) A stable pair(1) dim(F) ≤ 1 and F is pure;(2) s has zero-dimensional cokernel.The moduli scheme PT n (X, β) of stable pairs with fixing topological data [F] = β ∈ H 2 (X, Z), χ(F) = n is a scheme and the PT-invariant is defined by PT n,β (X) = χ(PT n (X, β), ν PT ), where ν PT is the Behrend function on PT n (X, β). Both DT-invariants and PT-invariants are curve counting invariants of X; The famous DT/PTcorrespondence conjecture in [43] equates these two invariants in terms of partition functions.The conjecture was proved by Bridgeland [9], and Toda [47] using the wall crossing idea, under which the DT-moduli space and the PT moduli space correspond to different (limit) stability conditions in Bridgeland's space of stability conditions.We pay more attention to Bridgeland's method for the proof. In [9] Bridgeland uses some Hall algebra identities in the motivic Hall algebra H(A) of the abelian category of coherent sheaves A = Coh(X); such that the DT-moduli space and the PT-moduli space are both elements in the Hall algebra. Then applying the integration map as in [33], [10] Bridgeland gets the DT/PT-correspondence.The same idea works for threefold flops. Let

show abstract

“…obtained by applying the renormalisation t → −r /2 t to Equation (4.4). According to [8, Section 1.1], the Hodge polynomial (more precisely, the Hodge series) of a cohomologically 6 For a cohomologically graded mixed Hodge structure , being of Tate type means that there exist integers a m ,n ∈ such that = m ,n ( ⊗n [n]) ⊕a m ,n , where = H c ( 1 , ), viewed as a pure Hodge structure of weight 2. See [8] for more details.…”

mentioning

confidence: 99%

Virtual classes and virtual motives of Quot schemes on threefolds

Ricolfi¹

2019

Preprint

View full text Add to dashboard Cite

For a simple, rigid vector bundle F on a Calabi-Yau 3-fold Y , we construct a symmetric obstruction theory on the Quot scheme Quot Y (F, n), and we solve the associated enumerative theory. We discuss the case of other 3-folds. Exploiting the critical structure on Quot 3 ( r , n), we construct a virtual motive (in the sense of Behrend-Bryan-Szendrői)for Quot Y (F, n) for an arbitrary vector bundle F on a smooth 3-fold Y . We compute the associated motivic partition function. We obtain new examples of higher rank (motivic) Donaldson-Thomas invariants. CONTENTS 0. Introduction 1 1. Preliminaries 3 2. Obstruction theories on Quot schemes 8 3. Higher rank Donaldson-Thomas invariants 17 4. The virtual motive of the Quot scheme 19 Appendix A. Obstruction theories 25 References 28

show abstract

On motivic vanishing cycles of critical loci

Cited by 19 publications

References 0 publications

Virtual fundamental classes for moduli spaces of sheaves on Calabi–Yau four-folds

Virtual fundamental classes for moduli spaces of sheaves on Calabi–Yau four-folds

Donaldson–Thomas invariants of Calabi–Yau orbifolds under flops

Virtual classes and virtual motives of Quot schemes on threefolds

Contact Info

Product

Resources

About