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Abstract We use the non-proper Morse theory of Palais–Smale to investigate the topology of smooth closed subvarieties of complex semi -abelian varieties and that of their infinite cyclic covers ...
A$$, it is a trivial fibration. If $$n\geq 2$$, then the fiber $$ K ^{[n]}:=\rho^{-1}(o_{A})$$ is a projective hyperkähler variety of dimension $$2(n-1)$$, called the $$n$$-th generalized Kummer variety associated ...
in Section 6 to classify integral special fibres of |${\mathbb{ K }}^*\times T$|-equivariant degenerations of rational projective complexity-one |$T$|- varieties . 2 Semi -Canonical Embeddings 2.1 |$T$|- varieties ...
Abstract We show that the main theorem of Morse theory holds for a large class of functions on singular spaces. The function must satisfy certain conditions extending the usual requirements ...
}$| as the second factor of |$ K \times \mathbb{T}$|). Going back to horospherical contractions of semi - projective varieties , we then show that the gradient flows associated with them now indeed give rise ...
topological entropy. 1 Introduction Throughout this note, we work in the category of projective varieties defined over |${\mathbb C}$|. The aim of this note is to give some affirmative answers (Theorems 1.7 ...
. Then it will be not hard to construct a perfectoid Shimura variety |$S_{ K ^p}(G,X)$| from |$S_{ K ^p}^0(G,X)$|, by using the theory of connected components of Shimura varieties (see the previous paragraph on our adaption ...
Abstract The goal of this article was to study the Iwasawa theory of an abelian variety $$A$$ that has complex multiplication by a complex multiplication (CM) field $$F$$ that contains the reflex ...
projective –injective objects. We call it the “ semi -derived Hall algebra”$$\mathcal {SDH}(\mathcal {F}, \mathcal {P}(\mathcal {F}))$$. We discuss its functoriality properties and show that it is a free module ...
variety , or a semi -algebraic set in k -dimensional affine or projective space, we study the isotypic decomposition of the $$\mathfrak{S}_{ k }$$-module $$\mathrm{H}^{\ast }(V,\mathbb{F})$$, where $$\mathbb{F ...
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