An invertible morphism of an algebraic variety or scheme into itself.

Ihackedit naruto blazingThe automorphism group of an algebraic variety is important for the concept of forms cf. Form of an algebraic variety.

For complete algebraic varieties over the field of complex numbers, the automorphism group is identical with the group of biholomorphic automorphisms. Algebraic curve. For automorphisms of surfaces, see Algebraic surface. Families of automorphisms are considered in the modern approach to automorphism groups of algebraic varieties. Representable functor by an algebraic group scheme with at most a countable number of connected components [3].

Grothendieck gave a proof of this fact for projective varieties, and this theorem has been extended to the case of proper flat schemes of morphisms. For incomplete varieties the automorphism functor is not always representable in the category of schemes.

For an affine variety, the automorphism functor is representable in the category of inductive limits of schemes. Apart from the simple case of the affine straight line, for the affine spaces only the automorphism group of the affine plane is known. It is a free product of two of its subgroups with as amalgamated subgroup their intersection, viz. For the treatment of affine algebraic surfaces transitively acted upon by the automorphism group, see [6].

Log in. Namespaces Page Discussion. Views View View source History. Jump to: navigationsearch. References [1] H. Matsumura, P. Monsky, "On the automorphisms of hypersurfaces" J.

Radio broadcasting script tagalog 2019Kyoto Univ.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Besides, the non-hyperbolic Riemann surfaces are the plane, the disk, the sphere, the annuli and the torii. If the automorphism group of a Riemann surface is transitive, the it must be of uncountable size since for any point p there must exist a distinct group element g p,q to carry it to each point q.

Also, even though the automorphism group of the disk is 1-transitive, as mentioned above Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. On the transitivity of the group of automorphisms of a Riemann surface Ask Question. Asked 7 years, 3 months ago. Active 1 year, 3 months ago. Viewed times. Edit : by Riemann surface, I mean connected complex holomorphic 1-dimensional manifold. Glougloubarbaki Glougloubarbaki 7, 1 1 gold badge 15 15 silver badges 43 43 bronze badges.

Does that mean that this number depends on the conformal structure more than the topology? Active Oldest Votes. Dan Asimov Dan Asimov 2 2 silver badges 4 4 bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.

Email Required, but never shown. Featured on Meta. Responding to the Lavender Letter and commitments moving forward.This result includes all previously known results for the density property of affine surfaces as special cases. We also give a description of the identity component of the group of holomorphic automorphisms of these surfaces.

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Index of /var/cache/stage/pools/cefxxtmrvf/j/uArzhantsev, I. Duke Math. Andrist, R. Proceedings of the American Mathematical Society, posted on Rafael, B. Fourier Grenoble 64 2— Dubouloz, A. Gizatullin, M. Donzelli, F. Flenner, H. Osaka University Press, Osaka Google Scholar. American Mathematical Society, Providence In: Ergebnisse der Mathematik und ihrer Grenzgebiete. A Series of Modern Surveys in Mathematics, vol. Springer, Heidelberg Kaliman, S.The density property for Gizatullin surfaces completed by four rational curves. Authors: Rafael B.

Abstract: Gizatullin surfaces completed by a zigzag of type can be described by the equationsand in where and are non-constant polynomials. We establish the algebraic density property for smooth Gizatullin surfaces of this type.

Moreover we also prove the density property for smooth surfaces given by these equations when and are holomorphic functions. References [Enhancements On Off] What's this?

### Infinite Transitivity on Affine Varieties

Additional Information Rafael B. Andrist and F. Kutzschebauch, The fibred density property and the automorphism group of the spectral ballMath. ArzhantsevH. FlennerS. KalimanF. Kutzschebauchand M. ZaidenbergFlexible varieties and automorphism groupsDuke Math. IMRN 2— DonzelliA. Dvorskyand S. KalimanAlgebraic density property of homogeneous spacesTransform.

Groups 15no. GizatullinQuasihomogeneous affine surfacesIzv. MR [7] M. Gizatullin and V. DanilovExamples of nonhomogeneous quasihomogeneous surfacesIzv. MR [8] M. DanilovAutomorphisms of affine surfaces. IIzv.

Xbox one minecraft modsPress, Osaka,pp. Lecture Notes, vol. A Series of Modern Surveys in Mathematics], vol. The homotopy principle in complex analysis. IMRN 21— Pure Appl. Algebrano. IIInternat.

References [1] Rafael B.In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.

Snooki archivesSkip to main content. This service is more advanced with JavaScript available. Advertisement Hide. Infinite Transitivity on Affine Varieties. Chapter First Online: 09 April This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, log in to check access. Arzhantsev, I. Google Scholar. Batyrev, V. Bogomolov, F. Borel, A. Danilov, V. USSR Izv. Dubouloz, A. Groups 14—, Flenner, H. Algebraic Geometry 20—, Freudenburg, G. SciencesSpringer, Berlin, Gizatullin, M. Kaliman, S.Automorphisms of -fibered affine surfaces.

Abstract: We develop techniques of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we associate to each surface of this type a graph encoding equivalence classes of rational fibrations from which it is possible to decide for instance if the automorphism group of is generated by automorphisms preserving these fibrations.

References [Enhancements On Off] What's this? Blanc unige. Blanc unibas. Dubouloz u-bourgogne. Shreeram S. Reine Angew. MR 2. Bandman and L. Pure Appl. Algebrano. DuboulozEmbeddings of Danielewski surfaces in affine spacesComment. Gizatullin and V. DanilovAutomorphisms of affine surfaces. IIzv. MR 7. IIIzv. MR 8. Press, Osaka,pp. MR GizatullinQuasihomogeneous affine surfacesIzv.

Heinrich W. Makar-LimanovOn groups of automorphisms of a class of surfacesIsrael J. Abhyankar, T. Moh, Embeddings of the line in the planeJ.

## Affine Surfaces With a Huge Group of Automorphisms

Bandman, L. Makar-Limanov, Affine surfaces with. Michigan Math. MR 3. Daigle, On locally nilpotent derivations ofJ. MR 4. Dubouloz, Completions of normal affine surfaces with a trivial Makar-Limanov invariantMichigan Math.

MR 5. Dubouloz, Embeddings of Danielewski surfaces in affine spacesComment.Skip to search form Skip to main content You are currently offline.

Some features of the site may not work correctly. DOI: Blanc and A. BlancA.

View PDF on arXiv. Save to Library. Create Alert. Launch Research Feed. Share This Paper. Top 3 of 6 Citations View All On automorphism groups of affine surfaces. Kovalenko, A. Perepechko, M. Zaidenberg A projective variety with discrete, non-finitely generated automorphism group. John Lesieutre Super-rigid affine Fano varieties. Cheltsov, A.

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View 1 excerpt, cites background. Research Feed. The density property for Gizatullin surfaces completed by four rational curves. Infinite transitivity and special automorphisms. View 2 excerpts, cites background. References Publications referenced by this paper. On groups of automorphisms of a class of surfaces.

Birational transformations of weighted graphs. Open Algebraic Surfaces.

**Graph automorphism**

Representability of group functors, and automorphisms of algebraic schemes.

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