Lifting differential operators from orbit spaces
Line bundles on the cotangent bundle fo the flag variety.
Line bundles on toroidal groups.
Linear bounds for levels of stable rationality
Let G be one of the groups SLn(ℂ), Sp2n (ℂ), SOm(ℂ), Om(ℂ), or G 2. For a generically free G-representation V, we say that N is a level of stable rationality for V/G if V/G × ℙN is rational. In this paper we improve known bounds for the levels of stable rationality for the quotients V/G. In particular, their growth as functions of the rank of the group is linear for G being one of the classical groups.
Linear models for reductive group actions on affine quadrics
Linear orbits of d-tuples of points in P1.
Linear systems representing threefolds which are scrolls on a rational surface.
Linear systems with multiple base points in .
Lines on Complete Intersection Threefolds with K=0.
Local properties of licci ideals.
Localization on singular varieties.
Locally complete intersection homomorphisms and a conjecture of Quillen on the vanishing of cotangent homology.
Loop groups and equations of KdV type
L'unirazionalità della varietà dei moduli delle curve di genere dodici
Mapping threefolds onto three-dimensional quadrics.
Mappings of the sets of invariant subspaces of null systems.
Maps of toric varieties in Cox coordinates
The Cox ring provides a coordinate system on a toric variety analogous to the homogeneous coordinate ring of projective space. Rational maps between projective spaces are described using polynomials in the coordinate ring, and we generalise this to toric varieties, providing a unified description of arbitrary rational maps between toric varieties in terms of their Cox coordinates. Introducing formal roots of polynomials is necessary even in the simplest examples.
Maximal compatible splitting and diagonals of Kempf varieties
Lakshmibai, Mehta and Parameswaran (LMP) introduced the notion of maximal multiplicity vanishing in Frobenius splitting. In this paper we define the algebraic analogue of this concept and construct a Frobenius splitting vanishing with maximal multiplicity on the diagonal of the full flag variety. Our splitting induces a diagonal Frobenius splitting of maximal multiplicity for a special class of smooth Schubert varieties first considered by Kempf. Consequences are Frobenius splitting of tangent bundles,...
Maximal rank curves and singular points of the Hilbert scheme
Maximal rationally connected fibrations and movable curves
A well known result of Miyaoka asserts that a complex projective manifold is uniruled if its cotangent bundle restricted to a general complete intersection curve is not nef. Using the Harder-Narasimhan filtration of the tangent bundle, it can moreover be shown that the choice of such a curve gives rise to a rationally connected foliation of the manifold. In this note we show that, conversely, a movable curve can be found so that the maximal rationally connected fibration of the manifold may be recovered...