A view on extending morphisms from ample divisors
نویسنده
چکیده
The philosophy that “a projective manifold is more special than any of its smooth hyperplane sections” was one of the classical principles of projective geometry. Lefschetz type results and related vanishing theorems were among the typically used techniques. We shall survey most of the problems, results and conjectures in this area, using the modern setting of ample divisors, and (some aspects of) Mori theory.
منابع مشابه
Three-dimensional Toric Morphisms with Anti-nef Canonical Divisors
In this paper, we classify projective toric birational morphisms from Gorenstein toric 3-folds onto the 3-dimensional affine space with relatively ample anti-canonical divisors.
متن کاملCYCLIC COVERING MORPHISMS ON M0,n
We study cyclic covering morphisms from M0,n to moduli spaces of unpointed stable curves of positive genus or compactified moduli spaces of principally polarized abelian varieties. Our main application is a construction of new semipositive vector bundles and nef divisors on M0,n, with a view toward the F-conjecture. In particular, we construct new extremal rays of Nef(M0,n/Sn). We also find an ...
متن کاملConformal Blocks Divisors on M 0,n from Sl 2
We study a family of semiample divisors on M 0,n defined using conformal blocks and analyze their associated morphisms.
متن کاملNEF DIVISORS ON M0,n FROM GIT
We introduce and study the GIT cone of M0,n, which is generated by the pullbacks of the natural ample line bundles on the GIT quotients (P)//SL(2). As one application, we prove unconditionally that the log canonical models of M0,n with a symmetric boundary divisor coincide with the moduli spaces of weighted curves or with the symmetric GIT quotient, extending the result of Matt Simpson.
متن کاملDegeneration of Kähler-Einstein Manifolds II: The Simple Toroidal Case
This work is a sequel of [6]. In algebraic geometry, when discussing the compactification of the moduli space of complex manifoldX with ample canonical bundle KX , it is necessary to consider holomorphic degeneration family π : X → B, where Xt = π (t) are smooth except for t = 0, such that the canonical bundle of Xt for t 6= 0 and the dualizing sheaf of X0 are ample. We will call such degenerat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009