Mini-workshop on Self-maps of Algebraic Varieties

 

 

March 28, 2019                       KIAS 8101

 

Titles/Abstracts Home > Titles/Abstracts

 

 

Keiji Oguiso

- Title: A surface in odd characteristic with discrete and non-finitely generated automorphism group
- Abstract: It was proved by Tien-Cuong Dinh and me that there is a smooth complex projective surface whose automorphism group is discrete and not finitely generated. In this talk, after recalling some known facts, I would like to show that there is a smooth projective surface, birational to some K3 surface, such that the automorphism group is discrete and not finitely generated, over any algebraically closed field of odd characteristic except precisely an algebraic closure of the prime field. I would like to discuss also higher dimensional examples as a corollary and a few related open questions.

 

Xun Yu

- Title: Minimum positive entropy of complex Enriques surface automorphisms

- Abstract: We determine the minimum positive entropy of complex Enriques surface automorphisms. This together with McMullen's work completes the determination of the minimum positive entropy of complex surface automorphisms in each class of Enriques-Kodaira classification of complex surfaces. As in McMullen's work, we finally reduce the problem to computer algebra. In this talk, after recalling known results and differences from Enriques case, I would like to explain how one can reduce this problem to finite computational problems which can be done by computer. This is a joint work with Professor Keiji Oguiso.

 

Eric Bedford

- Title: Conservative maps of compact, complex surfaces.

- Abstract: Let X be a rational surface, and let f be a biholomorphic automorphism of X. The Fatou set of f is the largest open subset of X where the iterates of f are equicontinuous. We say that f is conservative if there is a meromorphic 2-form w such that f*w = c w, where c is a complex number of modulus 1. In this talk, we will discuss properties of the Fatou set of a conservative map.

 

Eiichi Sato

- Title: On surjective morphisms between Fano varieties

- Abstract: For Fano varieties X, Y (dim X = dim Y > 2) we study whether there exists a surjective morphism f: X -> Y and what is the property, if exists. It is supposed that the source space X is a subvariety in projective space where it is covered by lines with the Picard number 1. Particularly we show that any surjective morphism from n (> 2)-dimensional smooth hypercubic to Fano variety Y is an isomorphism unless Y is projective space. These are stated by means of minimal free morphism (in Kollar's textbook) and the induced index.