Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces

Milena Hering; Benjamin Nill; Hendrik Süß

doi:10.1017/9781108877831

Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces

Milena Hering, Benjamin Nill, Hendrik Süß

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

Abstract

We give a combinatorial criterion for the tangent bundle on a smooth toric variety to be stable with respect to a given polarisation in terms of the corresponding lattice polytope. Furthermore, we show that for a smooth toric surface and a smooth toric variety of Picard rank 2, there exists an ample line bundle with respect to which the tangent bundle is stable if and only if it is an iterated blow-up of projective space.

Original language	English
Title of host publication	Facets of Algebraic Geometry
Subtitle of host publication	A Collection in Honor of William Fulton's 80th Birthday
Editors	Paolo Aluffi, David Anderson, Milena Hering, Mircea Mustata, Sam Payne
Publisher	Cambridge University Press
Number of pages	19
ISBN (Electronic)	9781108877831
DOIs	https://doi.org/10.1017/9781108877831
Publication status	Published - 2022

Publication series

Name	London Mathematical Society Lecture Note Series
Volume	472

Keywords / Materials (for Non-textual outputs)

math.AG
14J60 (Primary), 14M25 (Secondary)

Access to Document

10.1017/9781108877831

HeringNillSuessAccepted author manuscript, 466 KB
1910.08848v1Accepted author manuscript, 338 KB

Cite this

Hering, M., Nill, B., & Süß, H. (2022). Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces. In P. Aluffi, D. Anderson, M. Hering, M. Mustata, & S. Payne (Eds.), Facets of Algebraic Geometry: A Collection in Honor of William Fulton's 80th Birthday (London Mathematical Society Lecture Note Series; Vol. 472). Cambridge University Press. https://doi.org/10.1017/9781108877831

Hering, Milena ; Nill, Benjamin ; Süß, Hendrik. / Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces. Facets of Algebraic Geometry: A Collection in Honor of William Fulton's 80th Birthday. editor / Paolo Aluffi ; David Anderson ; Milena Hering ; Mircea Mustata ; Sam Payne. Cambridge University Press, 2022. (London Mathematical Society Lecture Note Series).

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abstract = " We give a combinatorial criterion for the tangent bundle on a smooth toric variety to be stable with respect to a given polarisation in terms of the corresponding lattice polytope. Furthermore, we show that for a smooth toric surface and a smooth toric variety of Picard rank 2, there exists an ample line bundle with respect to which the tangent bundle is stable if and only if it is an iterated blow-up of projective space. ",

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Hering, M, Nill, B & Süß, H 2022, Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces. in P Aluffi, D Anderson, M Hering, M Mustata & S Payne (eds), Facets of Algebraic Geometry: A Collection in Honor of William Fulton's 80th Birthday. London Mathematical Society Lecture Note Series, vol. 472, Cambridge University Press. https://doi.org/10.1017/9781108877831

Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces. / Hering, Milena; Nill, Benjamin; Süß, Hendrik.
Facets of Algebraic Geometry: A Collection in Honor of William Fulton's 80th Birthday. ed. / Paolo Aluffi; David Anderson; Milena Hering; Mircea Mustata; Sam Payne. Cambridge University Press, 2022. (London Mathematical Society Lecture Note Series; Vol. 472).

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

TY - CHAP

T1 - Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces

AU - Hering, Milena

AU - Nill, Benjamin

AU - Süß, Hendrik

PY - 2022

Y1 - 2022

N2 - We give a combinatorial criterion for the tangent bundle on a smooth toric variety to be stable with respect to a given polarisation in terms of the corresponding lattice polytope. Furthermore, we show that for a smooth toric surface and a smooth toric variety of Picard rank 2, there exists an ample line bundle with respect to which the tangent bundle is stable if and only if it is an iterated blow-up of projective space.

AB - We give a combinatorial criterion for the tangent bundle on a smooth toric variety to be stable with respect to a given polarisation in terms of the corresponding lattice polytope. Furthermore, we show that for a smooth toric surface and a smooth toric variety of Picard rank 2, there exists an ample line bundle with respect to which the tangent bundle is stable if and only if it is an iterated blow-up of projective space.

KW - math.AG

KW - 14J60 (Primary), 14M25 (Secondary)

U2 - 10.1017/9781108877831

DO - 10.1017/9781108877831

M3 - Chapter (peer-reviewed)

T3 - London Mathematical Society Lecture Note Series

BT - Facets of Algebraic Geometry

A2 - Aluffi, Paolo

A2 - Anderson, David

A2 - Hering, Milena

A2 - Mustata, Mircea

A2 - Payne, Sam

PB - Cambridge University Press

ER -

Hering M, Nill B, Süß H. Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces. In Aluffi P, Anderson D, Hering M, Mustata M, Payne S, editors, Facets of Algebraic Geometry: A Collection in Honor of William Fulton's 80th Birthday. Cambridge University Press. 2022. (London Mathematical Society Lecture Note Series). Epub 2022 Mar 31. doi: 10.1017/9781108877831

Stability of tangent bundles on smooth toric Picard-rank-2 varieties and surfaces

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Keywords / Materials (for Non-textual outputs)

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Cite this