ترغب بنشر مسار تعليمي؟ اضغط هنا

Equivariant birational geometry and modular symbols

79   0   0.0 ( 0 )
 نشر من قبل Yuri Tschinkel
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups.



قيم البحث

اقرأ أيضاً

We study the birational properties of geometrically rational surfaces from a derived categorical point of view. In particular, we give a criterion for the rationality of a del Pezzo surface over an arbitrary field, namely, that its derived category d ecomposes into zero-dimensional components. For del Pezzo surfaces of degree at least 5, we construct explicit semiorthogonal decompositions by subcategories of modules over semisimple algebras arising as endomorphism algebras of vector bundles and we show how to retrieve information about the index of the surface from Brauer classes and Chern classes associated to these vector bundles.
105 - Adrian Langer 2017
We study compactifications of Drinfeld half-spaces over a finite field. In particular, we construct a purely inseparable endomorphism of Drinfelds half-space $Omega (V)$ over a finite field $k$ that does not extend to an endomorphism of the projectiv e space $P (V)$. This should be compared with theorem of Remy, Thuillier and Werner that every $k$-automorphism of $Omega (V)$ extends to a $k$-automorphism of $P (V)$. Our construction uses an inseparable analogue of the Cremona transformation. We also study foliations on Drinfelds half-spaces. This leads to various examples of interesting varieties in positive characteristic. In particular, we show a new example of a non-liftable projective Calabi-Yau threefold in characteristic $2$ and we show examples of rational surfaces with klt singularities, whose cotangent bundle contains an ample line bundle.
175 - Bruno Kahn , R. Sujatha 2014
This version corrects a wrong proof of Proposition 6.3.2 and simplifies the exposition in Section 6.
In this paper we study smooth projective varieties and polarized pairs with an action of a one dimensional complex torus. As a main tool, we define birational geometric counterparts of these actions, that, under certain assumptions, encode the inform ation necessary to reconstruct them. In particular, we consider some cases of actions of low complexity -- measured in terms of two invariants of the action, called bandwidth and bordism rank -- and discuss how they are determined by well known birational transformations, namely Atiyah flips and Cremona transformations.
We develop a version of Hodge theory for a large class of smooth cohomologically proper quotient stacks $X/G$ analogous to Hodge theory for smooth projective schemes. We show that the noncommutative Hodge-de Rham sequence for the category of equivari ant coherent sheaves degenerates. This spectral sequence converges to the periodic cyclic homology, which we canonically identify with the topological equivariant $K$-theory of $X$ with respect to a maximal compact subgroup $M subset G$. The result is a natural pure Hodge structure of weight $n$ on $K^n_M(X^{an})$. We also treat categories of matrix factorizations for equivariant Landau-Ginzburg models.
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