10,697,289 research outputs found
Unramified Gromov-Witten and Gopakumar-Vafa invariants
No full textKim, Kresch and Oh defined unramified Gromov-Witten invariants. For a
threefold, Pandharipande conjectured that they are equal to Gopakumar-Vafa
invariants (BPS invariants) in the case of Fano classes and primitive
Calabi-Yau classes. We prove the conjecture using a wall-crossing technique.
This provides an algebro-geometric construction of Gopakumar-Vafa invariants in
these cases.Comment: 61 page
Gopakumar-Vafa Invariants and Macdonald Formula
No full textIn this paper, we present an investigation of the Gopakumar-Vafa (GV)
invariant, a curve-counting integral invariant associated with Calabi-Yau
threefolds, as proposed by physicists. Building upon the conjectural definition
of the GV invariant in terms of perverse sheaves, as formulated by Maulik-Toda
in 2016, we focus on the total space of the canonical bundle of
and compute the relevant invariants. We establish a conjectural correspondence
between the Gopakumar-Vafa and Pandharipande-Thomas invariants at the level of
perverse sheaves, drawing inspiration from the work of Migliorini, Shende, and
Viviani. This work serves as a significant step towards validating the
conjecture and deepening our understanding of the GV invariant and its
connections to algebraic geometry and physics
Some remarks on Gopakumar-Vafa invariants
No full textWe show that Gopakumar-Vafa invariants can be expressed in terms of the cohomology
ring of moduli space of D-branes without reference to the sl_2 \times sl_2 action. We also
give a simple construction of this action
A note on BPS structures and Gopakumar–Vafa invariants
No full textWe regard the work of Maulik and Toda, proposing a sheaf-theoretic approach to Gopakumar–Vafa invariants, as defining a BPS structure, that is, a collection of BPS invariants together with a central charge. Assuming their conjectures, we show that a canonical flat section of the flat connection corresponding to this BPS structure, at the level of formal power series, reproduces the Gromov–Witten partition function for all genera, up to some error terms in genus 0 and 1. This generalises a result of Bridgeland and Iwaki for the contribution from genus 0 Gopakumar–Vafa invariants
Cohomological X-independence for Higgs bundles and Gopakumar–Vafa invariants
No full textThe aim of this paper is two-fold. Firstly, we prove Toda’s X-independence conjecture for Gopakumar–Vafa invariants of arbitrary local curves. Secondly, following Davison’s work, we introduce the BPS cohomology for moduli spaces of Higgs bundles of rank r and Euler characteristic X which are not necessary coprime, and show that it does not depend on X. This result extends the Hausel–Thaddeus conjecture on the X-independence of E-polynomials proved by Mellit, Groechenig–Wyss–Ziegler and Yu in two ways: We obtain an isomorphism of mixed Hodge modules on the Hitchin base rather than an equality of E-polynomials, and we do not need the coprime assumption. The proof of these results is based on a description of the moduli stack of one-dimensional coherent sheaves on a local curve as a global critical locus which is obtained in the companion paper by the first author and Naruki Masuda
Stable pairs and Gopakumar-Vafa type invariants on holomorphic symplectic 4-folds
No full textAs an analogy to Gopakumar-Vafa conjecture on Calabi-Yau 3-folds,
Klemm-Pandharipande defined Gopakumar-Vafa type invariants of a Calabi-Yau
4-fold using Gromov-Witten theory. When is holomorphic symplectic,
Gromov-Witten invariants vanish and one can consider the corresponding reduced
theory. In a companion work, we propose a definition of Gopakumar-Vafa type
invariants for such a reduced theory. In this paper, we give them a sheaf
theoretic interpretation via moduli spaces of stable pairs.Comment: 25 pages. Published version. arXiv admin note: text overlap with
arXiv:2201.1087
Integrality of genus zero Gopakumar-Vafa type invariants of semi-positive varieties
No full textWe give an alternate proof of the integrality conjecture of genus zero
Gopakumar-Vafa type invariants on semi-positive varieties using algebraic
geometry. The main technique is to relate Gopakumar-Vafa type invariants to
quantum -invariants and to utilize the integrality of the latter.Comment: corrected the computation on Proposition 3.
Gopakumar-Vafa Hierarchies in Winding Inflation and Uplifts
No full textWe propose a combined mechanism to realize both winding inflation and de Sitter uplifts. We realize the necessary structure of competing terms in the scalar potential not via tuning the vacuum expectation values of the complex structure moduli, but by a hierarchy of the Gopakumar-Vafa invariants of the underlying Calabi-Yau threefold. To show that Calabi-Yau threefolds with the prescribed hierarchy actually exist, we explicitly create a database of all the genus Gopakumar-Vafa invariants up to total degree for all the complete intersection Calabi-Yau's up to Picard number . As a side product, we also identify all the redundancies present in the CICY list, up to Picard number . Both databases can be accessed at this link: https://www.desy.de/~westphal/GV_CICY_webpage/GVInvariants.html
Gopakumar-Vafa invariant and Macdonald formula
No full textIn this thesis, I will introduce the Gopakumar-Vafa(GV) invariant and show one calculation on the nonreduced cycle. The GV invariant is an integral invariant predicted by physicist that counts the number of curves inside a given Calabi-Yau threefold. The definition has been conjectured by Maulik-Toda in 2016 in terms of perverse sheaf. I will use this definition on the total space of canonical bundle of P2 and compute the associated invariants. I will introduce a Gopakumar-Vafa/Pandharipande-Thomas correspondence on the level of perverse sheaves, inspired by the work of Migliorini-Shende-Viviani. I will verify that my calculation actually proves part of the conjecture. I have shown a strong evidence for this conjecture in the case of degree 2.Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-01-12 without embargo termsThe student, Lutian Zhao, accepted the attached license on 2021-07-12 at 13:02.The student, Lutian Zhao, submitted this Dissertation for approval on 2021-07-12 at 13:06.This Dissertation was approved for publication on 2021-07-14 at 17:10.DSpace SAF Submission Ingestion Package generated from Vireo submission #16850 on 2022-01-12 at 12:44:54Made available in DSpace on 2022-01-12T21:45:36Z (GMT). No. of bitstreams: 3
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Previous issue date: 2021-07-1
Installing Automobility
No full textAn examination of the process of prioritizing private motorized transportation in Bengaluru, a rapidly growing megacity of the Global South. Automobiles and their associated infrastructures, deeply embedded in Western cities, have become a rapidly growing presence in the mega-cities of the Global South. Streets once crowded with pedestrians, pushcarts, vendors, and bicyclists are now choked with motor vehicles, many of them private automobiles. In this book, Govind Gopakumar examines this shift, analyzing the phenomenon of automobility in Bengaluru (formerly known as Bangalore), a rapidly growing city of about ten million people in southern India. He finds that the advent of automobility in Bengaluru has privileged the mobility needs of the elite while marginalizing those of the rest of the population. Gopakumar connects Bengaluru's burgeoning automobility to the city's history and to the spatial, technological, and social interventions of a variety of urban actors. Automobility becomes a juggernaut, threatening to reorder the city to enhance automotive travel. He discusses the evolution of congestion and urban change in Bengaluru; the “regimes of congestion” that emerge to address the issue; an “infrastructurescape” that shapes the mobile behavior of all residents but is largely governed by the privileged; and the enfranchisement of an “automotive citizenship” (and the disenfranchisement of non-automobile-using publics). Gopakumar also finds that automobility in Bengaluru faces ongoing challenges from such diverse sources as waste flows, popular religiosity, and political leadership. These challenges, however, introduce messiness without upsetting automobility. He therefore calls for efforts to displace automobility that are grounded in reordering the mobility regime, relandscaping the city and its infrastructures, and reclaiming streets for other uses
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