On the theory of differentials on algebraic varieties
5
Citation
12
Reference
10
Related Paper
Citation Trend
Keywords:
Algebraic variety
We show that if the degree of a nonsingular projective variety is high enough, maximization of any of the most important numerical invariants, such as class, Betti number, and any of the Chern or middle Hodge numbers, leads to the same class of extremal varieties. Moreover, asymptotically (say, for varieties whose total Betti number is big enough) the ratio of any two of these invariants tends to a well-defined constant.
Algebraic variety
Projective variety
Constant (computer programming)
Cite
Citations (3)
Cite
Citations (0)
Cite
Citations (1)
This is a long overdue write up of the following: If the fundamental group of a normal complex algebraic variety (respectively Zariski open subset of a compact Kähler manifold) is a solvable group of matrices over Q (respectively polycyclic group), then it is virtually nilpotent. This should be interpreted as saying that a large class of solvable groups will not occur as fundamental groups of such spaces. The essential strategy is to first "complete" these groups to algebraic groups (generalizing constructions of Malcev and Mostow), and then check that the identity component is unipotent. This is done by Galois theoretic methods in the algebraic case, and is reduced to homological properties of one dimensional characters in the analytic case.
Cite
Citations (7)
Our main purpose is to introduce the notion of almost α(Λ, sp)-continuous multifunctions. Moreover, some characterizations of almost α(Λ, sp)-continuous multifunctions are established.
Cite
Citations (5)
Cite
Citations (33)
In this chapter we develop the necessary machinery for working with Segre varieties associated with real analytic hypersurfaces and give some immediate applications. In particular, we show that a germ of a biholomorphic map between Levi nondegenerate algebraic hypersurfaces is necessarily algebraic.
Algebraic variety
Cite
Citations (0)
Inspired by the work of Cherry, we introduce and study a new notion of Brody hyperbolicity for rigid analytic varieties over a non-archimedean field $K$ of characteristic zero. We use this notion of hyperbolicity to show the following algebraic statement: if a projective variety admits a non-constant morphism from an abelian variety, then so does any specialization of it. As an application of this result, we show that the moduli space of abelian varieties is $K$-analytically Brody hyperbolic in equal characteristic zero. These two results are predicted by the Green-Griffiths-Lang conjecture on hyperbolic varieties and its natural analogues for non-archimedean hyperbolicity. Finally, we use Scholze's uniformization theorem to prove that the aforementioned moduli space satisfies a non-archimedean analogue of the "Theorem of the Fixed Part" in mixed characteristic.
Morphism
Abelian variety
Projective variety
Algebraic variety
Zero (linguistics)
Cite
Citations (13)
Cite
Citations (4)
Characterization
Algebraic variety
Cite
Citations (156)