منابع مشابه
Valuations and plurisubharmonic singularities
We extend to higher dimension our valuative analysis of singularities of psh functions started in [FJ2]. Following [KoSo], we describe the geometry of the space V of all normalized valuations on C[z1, . . . , zn] centered at the origin. It is a union of simplices naturally endowed with an affine structure. Using relative positivity properties of divisors living on modifications of C n over the ...
متن کاملPlurisubharmonic functions and their singularities
The theme of these lectures is local and global properties of plurisubharmonic functions. First differential inequalities defining convex, subharmonic and plurisubharmonic functions are discussed. It is proved that the marginal function of a plurisubharmonic function is plurisubharmonic under certain hypotheses. We study the singularities of plurisubharmonic functions using methods from convexi...
متن کاملPlurisubharmonic functions with logarithmic singularities
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متن کاملMaximal Plurisubharmonic Models
An analytic pair of dimension n and center V is a pair (V,M) where M is a complex manifold of (complex) dimension n and V ⊂ M is a closed totally real analytic submanifold of dimension n. To an analytic pair (V,M) we associate the class U (V,M) of the functions u : M → [0,π/4[ which are plurisubharmonic in M and such that u(p)= 0 for each p ∈ V . If U (V,M) admits a maximal function u, the trip...
متن کاملPlurisubharmonic Domination
A common device in several complex variables, notably in the theory of Stein spaces, is to exhaust a space S by a sequence of holomorphically convex compact subsets Kj . Analytical problems one has to solve on S (say, a Cousin problem) tend to become more manageable when restricted to Kj because over compact sets the data is uniformly controlled; on the other hand, once the problem is solved on...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 2012
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap106-0-20