ar X iv : m at h / 07 03 13 1 v 1 [ m at h . A G ] 5 M ar 2 00 7 TOWARDS NON - REDUCTIVE GEOMETRIC INVARIANT THEORY

نویسنده

  • FRANCES KIRWAN
چکیده

We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal for us is to understand the cohomology of “quotients” under such actions, by generalizing (from reductive to non-reductive group actions) existing methods involving Mumford’s geometric invariant theory (GIT). We concentrate on actions of unipotent groups H, and define sets of stable points X and semistable points X, often explicitly computable via the methods of reductive GIT, which reduce to the standard definitions due to Mumford in the case of reductive actions. We compare these with definitions in the literature. Results include (1) a geometric criterion determining whether or not a ring of invariants is finitely generated, (2) the existence of a geometric quotient of X, and (3) the existence of a canonical “enveloping quotient” variety of X, denoted X//H, which (4) has a projective completion given by a reductive GIT quotient and (5) is itself projective and isomorphic to Proj(k[X]) when k[X] is finitely generated.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ar X iv : m at h / 01 03 02 6 v 2 [ m at h . A G ] 7 M ar 2 00 1 TENSOR PRODUCT VARIETIES AND CRYSTALS GL CASE

A geometric theory of tensor product for glN -crystals is described. In particular, the role of Spaltenstein varieties in the tensor product is explained. As a corollary a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain tensor product multiplicity) is obtained.

متن کامل

ar X iv : m at h / 03 06 23 5 v 2 [ m at h . D G ] 8 N ov 2 00 6 GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD

We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16] and [19] by a certain fractional power of the abelian theory first considered in [13] and further studied in [2].

متن کامل

ar X iv : m at h / 05 11 30 0 v 1 [ m at h . A G ] 1 1 N ov 2 00 5 Typical separating invariants

It is shown that a trivial version of polarization is sufficient to produce separating systems of polynomial invariants: if two points in the direct sum of the G–modules W and m copies of V can be separated by polynomial invariants, then they can be separated by invariants depending only on ≤ 2 dim(V ) variables of type V ; when G is reductive, invariants depending only on ≤ dim(V ) + 1 variabl...

متن کامل

ar X iv : m at h / 02 03 15 3 v 1 [ m at h . O C ] 1 5 M ar 2 00 2 CONTROLLABILITY OF REDUCED SYSTEMS

Sufficient conditions for the controllability of a conservative reduced system are given. Several examples illustrating the theory are also presented.

متن کامل

ar X iv : m at h / 03 06 23 5 v 1 [ m at h . D G ] 1 6 Ju n 20 03 GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY JØRGEN

We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [48] and [51] by a certain fractional power of the abelian theory first considered in [32] and further studied in [2].

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008