Flexible affine cones and flexible coverings

Mateusz Michalek; Alexander Perepechko; Hendrik Suess

doi:10.1007/s00209-018-2069-2

Flexible affine cones and flexible coverings

Mateusz Michalek^*, Alexander Perepechko, Hendrik Suess

^*Corresponding author for this work

Not published at Aalto University

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

11 Citations (Scopus)

Abstract

We provide a new criterion for flexibility of affine cones over varieties covered by flexible affine varieties. We apply this criterion to prove flexibility of affine cones over secant varieties of Segre-Veronese embeddings and over certain Fano threefolds. We further prove flexibility of total coordinate spaces of Cox rings of del Pezzo surfaces.

Original language	English
Pages (from-to)	1457-1478
Number of pages	22
Journal	MATHEMATISCHE ZEITSCHRIFT
Volume	290
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-018-2069-2
Publication status	Published - Dec 2018
MoE publication type	A1 Journal article-refereed

Keywords

Automorphism group
Transitivity
Flexibility
Affine cone
Cox ring
Segre-Veronese embedding
Secant variety
Del Pezzo surface
DEL-PEZZO SURFACES
TORUS ACTIONS
COX RINGS
INFINITE TRANSITIVITY
POLYHEDRAL DIVISORS
UNIVERSAL TORSORS
COMPLEXITY ONE
T-VARIETIES
SINGULARITIES
CLASSIFICATION

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10.1007/s00209-018-2069-2

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title = "Flexible affine cones and flexible coverings",

abstract = "We provide a new criterion for flexibility of affine cones over varieties covered by flexible affine varieties. We apply this criterion to prove flexibility of affine cones over secant varieties of Segre-Veronese embeddings and over certain Fano threefolds. We further prove flexibility of total coordinate spaces of Cox rings of del Pezzo surfaces.",

keywords = "Automorphism group, Transitivity, Flexibility, Affine cone, Cox ring, Segre-Veronese embedding, Secant variety, Del Pezzo surface, DEL-PEZZO SURFACES, TORUS ACTIONS, COX RINGS, INFINITE TRANSITIVITY, POLYHEDRAL DIVISORS, UNIVERSAL TORSORS, COMPLEXITY ONE, T-VARIETIES, SINGULARITIES, CLASSIFICATION",

author = "Mateusz Michalek and Alexander Perepechko and Hendrik Suess",

year = "2018",

month = dec,

doi = "10.1007/s00209-018-2069-2",

language = "English",

volume = "290",

pages = "1457--1478",

journal = "MATHEMATISCHE ZEITSCHRIFT",

issn = "0025-5874",

publisher = "Springer",

number = "3-4",

}

TY - JOUR

T1 - Flexible affine cones and flexible coverings

AU - Michalek, Mateusz

AU - Perepechko, Alexander

AU - Suess, Hendrik

PY - 2018/12

Y1 - 2018/12

N2 - We provide a new criterion for flexibility of affine cones over varieties covered by flexible affine varieties. We apply this criterion to prove flexibility of affine cones over secant varieties of Segre-Veronese embeddings and over certain Fano threefolds. We further prove flexibility of total coordinate spaces of Cox rings of del Pezzo surfaces.

AB - We provide a new criterion for flexibility of affine cones over varieties covered by flexible affine varieties. We apply this criterion to prove flexibility of affine cones over secant varieties of Segre-Veronese embeddings and over certain Fano threefolds. We further prove flexibility of total coordinate spaces of Cox rings of del Pezzo surfaces.

KW - Automorphism group

KW - Transitivity

KW - Flexibility

KW - Affine cone

KW - Cox ring

KW - Segre-Veronese embedding

KW - Secant variety

KW - Del Pezzo surface

KW - DEL-PEZZO SURFACES

KW - TORUS ACTIONS

KW - COX RINGS

KW - INFINITE TRANSITIVITY

KW - POLYHEDRAL DIVISORS

KW - UNIVERSAL TORSORS

KW - COMPLEXITY ONE

KW - T-VARIETIES

KW - SINGULARITIES

KW - CLASSIFICATION

U2 - 10.1007/s00209-018-2069-2

DO - 10.1007/s00209-018-2069-2

M3 - Article

SN - 0025-5874

VL - 290

SP - 1457

EP - 1478

JO - MATHEMATISCHE ZEITSCHRIFT

JF - MATHEMATISCHE ZEITSCHRIFT

IS - 3-4

ER -

Flexible affine cones and flexible coverings

Abstract

Keywords

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