# Flexible affine cones and flexible coverings

@article{Michaek2018FlexibleAC, title={Flexible affine cones and flexible coverings}, author={Mateusz Michałek and Alexander Perepechko and Hendrik S{\"u}{\ss}}, journal={Mathematische Zeitschrift}, year={2018}, volume={290}, pages={1457-1478} }

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.

## 12 Citations

### Affine cones over cubic surfaces are flexible in codimension one

- MathematicsForum Mathematicum
- 2020

Abstract Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension…

### Flexibility of Affine cones over Mukai fourfolds of genus $g\ge7$

- Mathematics, Biology
- 2022

We show that the affine cones over a general Fano-Mukai fourfold of genus g = 7, 8 and 9 are flexible. Equivalently, there is an infinitely transitive action of the special automorphism group on such…

### Affine cones over Fano-Mukai fourfolds of genus 10 are flexible

- Mathematics
- 2020

We show that the affine cones over any Fano--Mukai fourfold of genus 10 are flexible;
in particular, the automorphism group of such a cone acts highly transitively outside the vertex.
Furthermore,…

### Secant varieties of toric varieties arising from simplicial complexes

- MathematicsLinear Algebra and its Applications
- 2020

### Cohen–Macaulay and Gorenstein tangential varieties of the Segre–Veronese varieties

- MathematicsBulletin of the London Mathematical Society
- 2022

We classify the tangential varieties of the Segre–Veronese varieties which are Cohen–Macaulay or Gorenstein.

### Recent developments on Oka manifolds

- Mathematics
- 2020

A BSTRACT . This paper is a survey of developments in Oka theory since the publication of my book Stein Manifolds and Holomorphic Mappings (The Homotopy Principle in Complex Analysis) , Second…

### Infinite transitivity, finite generation, and Demazure roots

- MathematicsAdvances in Mathematics
- 2019

### Cylinders in Fano varieties

- MathematicsEMS Surveys in Mathematical Sciences
- 2021

. This paper is a survey about cylinders in Fano varieties and related problems.

### J 45 Fano varieties 14 J 50 Automorphisms of surfaces and higher-dimensional varieties 14 R 20 Group actions on affine varieties 14 R 25 Affine fibrations 14 E 08 Rationality questions in algebraic geometry 14 E 30 Minimal

- Mathematics
- 2021

References: [1] H. Ahmadinezhad, I. Cheltsov, and J. Schicho, On a conjecture of Tian.Math. Z.288(2018), no. 1-2, 217-241 Zbl1390.14109MR3774411 · Zbl 1390.14109 [2] J. Alper, H. Blum, D.…

### Fano-Mukai fourfolds of genus 10 as compactifications of ℂ^4

- Mathematics
- 2017

It is known that the moduli space of smooth Fano-Mukai fourfolds V18 of genus 10 has dimension one. We show that any such fourfold is a completion of C in two different ways. Up to isomorphism, there…

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