ترغب بنشر مسار تعليمي؟ اضغط هنا

A remark on the rank of finite $p$-groups of birational automorphisms

109   0   0.0 ( 0 )
 نشر من قبل Jinsong Xu
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English
 تأليف Jinsong Xu




اسأل ChatGPT حول البحث

We improve a result of Prokhorov and Shramov on the rank of finite $p$-subgroups of the birational automorphism group of a rationally connected variety. Known examples show that they are sharp in many cases.



قيم البحث

اقرأ أيضاً

212 - Jinsong Xu 2018
We study finite $p$-subgroups of birational automorphism groups. By virtue of boundedness theorem of Fano varieties, we prove that there exists a constant $R(n)$ such that a rationally connected variety of dimension $n$ over an algebraically closed f ield is rational if its birational automorphism group contains a $p$-subgroups of maximal rank for $p > R(n)$. Some related applications on Jordan property are discussed.
We show that if a group automorphism of a Cremona group of arbitrary rank is also a homeomorphism with respect to either the Zariski or the Euclidean topology, then it is inner up to a field automorphism of the base-field. Moreover, we show that a si milar result holds if we consider groups of polynomial automorphisms of affine spaces instead of Cremona groups.
72 - Christian Urech 2018
We classify simple groups that act by birational transformations on compact complex Kahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective surface over an arbitrary field is finite.
We classify a large class of small groups of finite Morley rank: $N_circ^circ$-groups which are the infinite analogues of Thompsons $N$-groups. More precisely, we constrain the $2$-structure of groups of finite Morley rank containing a definable, normal, non-soluble, $N_circ^circ$-subgroup.
The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank, although the same questions can be asked about other classes of objects, for example, groups definable in $omega$-stable and $o$-minimal theories. In many cases, answers are not known even in the classical category of algebraic groups over algebraically closed fields.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا