A note on a question of Markman

Shengyuan Huang

doi:10.1016/j.jpaa.2021.106673

A note on a question of Markman

Shengyuan Huang

Mathematics

Research output: Contribution to journal › Article › peer-review

58 Downloads (Pure)

Abstract

Let ℱ be a vector bundle on a complex projective algebraic variety X. If ℱ deforms along a first order deformation of X, its Mukai vector remains of Hodge type along this deformation. We prove an analogous statement for all polyvector fields, not only for those in H¹ (X, T_x) corresponding to deformations of the complex structure. This answers a question of Markman. We also explore a Lie theoretic analogue of the statement above.

Original language	English
Article number	106673
Number of pages	8
Journal	Journal of Pure and Applied Algebra
Volume	225
Issue number	9
Early online date	7 Jan 2021
DOIs	https://doi.org/10.1016/j.jpaa.2021.106673
Publication status	Published - Sept 2021

Keywords

Hochschild homology and cohomology
HKR isomorphisms
Deformation

Access to Document

10.1016/j.jpaa.2021.106673Licence: None: All rights reserved

HuangS2021noteAccepted author manuscript, 224 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

Cite this

@article{e9daa5634f114ed5b8f3d4eb05db5b32,

title = "A note on a question of Markman",

abstract = "Let ℱ be a vector bundle on a complex projective algebraic variety X. If ℱ deforms along a first order deformation of X, its Mukai vector remains of Hodge type along this deformation. We prove an analogous statement for all polyvector fields, not only for those in H1 (X, Tx) corresponding to deformations of the complex structure. This answers a question of Markman. We also explore a Lie theoretic analogue of the statement above.",

keywords = "Hochschild homology and cohomology, HKR isomorphisms, Deformation",

author = "Shengyuan Huang",

year = "2021",

month = sep,

doi = "10.1016/j.jpaa.2021.106673",

language = "English",

volume = "225",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier",

number = "9",

}

TY - JOUR

T1 - A note on a question of Markman

AU - Huang, Shengyuan

PY - 2021/9

Y1 - 2021/9

N2 - Let ℱ be a vector bundle on a complex projective algebraic variety X. If ℱ deforms along a first order deformation of X, its Mukai vector remains of Hodge type along this deformation. We prove an analogous statement for all polyvector fields, not only for those in H1 (X, Tx) corresponding to deformations of the complex structure. This answers a question of Markman. We also explore a Lie theoretic analogue of the statement above.

AB - Let ℱ be a vector bundle on a complex projective algebraic variety X. If ℱ deforms along a first order deformation of X, its Mukai vector remains of Hodge type along this deformation. We prove an analogous statement for all polyvector fields, not only for those in H1 (X, Tx) corresponding to deformations of the complex structure. This answers a question of Markman. We also explore a Lie theoretic analogue of the statement above.

KW - Hochschild homology and cohomology

KW - HKR isomorphisms

KW - Deformation

U2 - 10.1016/j.jpaa.2021.106673

DO - 10.1016/j.jpaa.2021.106673

M3 - Article

SN - 0022-4049

VL - 225

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 9

M1 - 106673

ER -

A note on a question of Markman

Abstract

Keywords

Access to Document

Fingerprint

Cite this