Frobenius Splittings

نویسنده

  • Wilberd van der Kallen
چکیده

Frobenius splittings were introduced by V. B. Mehta and A. Ramanathan in [6] and refined further by S. Ramanan and Ramanathan in [9]. Frobenius splittings have proven to be a amazingly effective when they apply. Proofs involving Frobenius splittings tend to be very efficient. Other methods usually require a much more detailed knowledge of the object under study. For instance, while showing that the intersection of one union of Schubert varieties with another union of Schubert varieties is reduced, one does not need to know where that intersection is situated, let alone what it looks like exactly. Before getting to serious applications we slowly introduce the main concepts.

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

Frobenius Splittings of Toric Varieties

We discuss a characteristic free version of Frobenius splittings for toric varieties and give a polyhedral criterion for a toric variety to be diagonally split. We apply this criterion to show that section rings of nef line bundles on diagonally split toric varieties are normally presented and Koszul, and that Schubert varieties are not diagonally split in general.

متن کامل

On the B-canonical Splittings of Flag Varieties

Let G be a semisimple algebraic group over an algebraically closed field of positive characteristic. In this note, we show that an irreducible closed subvariety of the flag variety of G is compatibly split by the unique canonical Frobenius splitting if and only if it is a Richardson variety, i.e. an intersection of a Schubert and an opposite Schubert variety.

متن کامل

Steinberg Modules and Donkin Pairs

We prove that in characteristic p > 0 a module with good filtration for a group of type E6 restricts to a module with good filtration for a group of type F4. Thus we confirm a conjecture of Brundan for one more case. Our method relies on the canonical Frobenius splittings of Mathieu. Next we settle the remaining cases, in characteristic not 2, with a computer-aided variation on the old method o...

متن کامل

Generalizations of M-matrices which may not have a nonnegative inverse

Generalizations of M -matrices are studied, including the new class of GM -matrices. The matrices studied are of the form sI−B with B having some Perron-Frobenius property, but not necessarily being nonnegative. Results for these classes of matrices are shown, which are analogous to those known for M -matrices. Also, various splittings of a GM -matrix are studied along with conditions for their...

متن کامل

Frobenius kernel and Wedderburn's little theorem

We give a new proof of the well known Wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎We apply the concept of Frobenius kernel in Frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

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 2013