Limits of Calabi–Yau metrics when the Kähler class degenerates
Limits of Hodge Structures.
Limits of log canonical thresholds
Let denote the set of log canonical thresholds of pairs , with a nonsingular variety of dimension , and a nonempty closed subscheme of . Using non-standard methods, we show that every limit of a decreasing sequence in lies in , proving in this setting a conjecture of Kollár. We also show that is closed in ; in particular, every limit of log canonical thresholds on smooth varieties of fixed dimension is a rational number. As a consequence of this property, we see that in order to check...
Line bundles on arithmetic surfaces and intersection theory.
Line bundles on the cotangent bundle fo the flag variety.
Line bundles on toroidal groups.
Line bundles with partially vanishing cohomology
Define a line bundle on a projective variety to be -ample, for a natural number , if tensoring with high powers of kills coherent sheaf cohomology above dimension . Thus 0-ampleness is the usual notion of ampleness. We show that -ampleness of a line bundle on a projective variety in characteristic zero is equivalent to the vanishing of an explicit finite list of cohomology groups. It follows that -ampleness is a Zariski open condition, which is not clear from the definition.
Linear bound for abelian automorphisms of varieties of general type.
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 Complementary Inequalities for Orders of Germs of Analytic Functions.
Linear equivalence of Tango bundles on P4.
Linear Forms in Elliptic Integrals.
Linear forms on abelian varieties over local fields
Linear forms on arithmetic abelian varieties: ineffective bounds
Linear Fractional Recurrences: Periodicities and Integrability
Linear fractional recurrences are given as , where and are linear functions of . In this article we consider two questions about these recurrences: (1) Find and such that the recurrence is periodic; and (2) Find (invariant) integrals in case the induced birational map has quadratic degree growth. We approach these questions by considering the induced birational map and determining its dynamical degree. The first theorem shows that for each there are -step linear fractional recurrences...
Linear free divisors and the global logarithmic comparison theorem
A complex hypersurface in is a linear free divisor (LFD) if its module of logarithmic vector fields has a global basis of linear vector fields. We classify all LFDs for at most .By analogy with Grothendieck’s comparison theorem, we say that the global logarithmic comparison theorem (GLCT) holds for if the complex of global logarithmic differential forms computes the complex cohomology of . We develop a general criterion for the GLCT for LFDs and prove that it is fulfilled whenever the...
Linear maps preserving orbits
Let be a connected complex reductive group where is a finite-dimensional complex vector space. Let and let . Following Raïs we say that the orbit is characteristic for if the identity component of is . If is semisimple, we say that is semi-characteristic for if the identity component of is an extension of by a torus. We classify the -orbits which are not (semi)-characteristic in many cases.
Linear models for reductive group actions on affine quadrics
Linear orbits of d-tuples of points in P1.
Linear Spaces on the Intersection of Cubic Hypersurfaces.