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Titlebook: Automorphisms in Birational and Affine Geometry; Levico Terme, Italy, Ivan Cheltsov,Ciro Ciliberto,Mikhail Zaidenberg Conference proceeding

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Singular del Pezzo Fibrations and Birational Rigidityionally rigid if and only if its anticanonical class is an interior point in the cone of mobile divisors. The conjecture is proved to be true for smooth models (with a generality assumption for degree 3). It is speculated that the conjecture holds for, at least, Gorenstein models in degree 1 and 2.
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On Automorphisms and Endomorphisms of Projective Varietiesive variety. Then we show that very few connected algebraic semigroups can be realized as endomorphisms of some projective variety ., by describing the structure of all connected subsemigroup schemes of End(.).
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On the Genus of Birational Maps Between Threefoldsthe definition introduced by Frumkin [Mat. Sb. (N.S.) 90(132):196–213, 325, 1973], and the second one was recently suggested to me by S. Cantat. By focusing first on proving that these two definitions are equivalent, one can obtain all the results in M.A. Frumkin [Mat. Sb. (N.S.) 90(132):196–213, 32
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On the Automorphisms of Moduli Spaces of Curvesves have been extensively studied by A. Bruno and the authors. In this paper we give a survey of these recent results and extend our techniques to some moduli spaces appearing as intermediate steps of Kapranov’s and Keel’s realizations of ., and to the degenerations of Hassett’s spaces obtained by a
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Birational Automorphism Groups of Projective Varieties of Picard Number Twou manifolds of Picard number 2 to arbitrary singular varieties . (resp. to klt Calabi–Yau pairs in broad sense) of Picard number 2. When . has only klt singularities and is not a complex torus, we show that either Aut(.) is almost infinite cyclic, or it has only finitely many connected components.
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The Jacobian Conjecture, Together with Specht and Burnside-Type Problemsexander Vladimirovich Yagzhev (1951–2001), whose works have only been partially published. This approach also indicates some very close connections between mathematical physics, universal algebra, and automorphisms of polynomial algebras.
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Equivariant Triviality of Quasi-Monomial Triangular ,-Actions on ,tions are translations whenever they are proper. The argument, which is based on explicit techniques, provides an illustration of the difficulties encountered and an introduction to the more abstract methods which were used recently by the authors to solve the general triangular case.
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