The finiteness of compact varieties in
Walter Rudin (1981)
Annales Polonici Mathematici
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Walter Rudin (1981)
Annales Polonici Mathematici
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Luca Chiantini, Ciro Ciliberto (2010)
Journal of the European Mathematical Society
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In this paper we generalize Zak’s theorems on tangencies and on linear normality as well as Zak’s definition and classification of Severi varieties. In particular we find sharp lower bounds for the dimension of higher secant varieties of a given variety under suitable regularity assumptions on , and we classify varieties for which the bound is attained.
K. Denecke (1988)
Banach Center Publications
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Antonio Lanteri, Daniele Struppa (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Si illustrano alcune relazioni tra le varietà proiettive complesse con duale degenere, le varietà la cui topologia si riflette in quella della sezione iperpiana in misura maggiore dell'ordinario e le varietà fibrate in spazi lineari su di una curva.
A. Huckleberry, H. Sebert (2013)
Annales de l’institut Fourier
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Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities for eigensections approaching a semiclassical ray. Here is a normal compact toric variety and is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate...
Martin G. Gulbrandsen (2007)
Bulletin de la Société Mathématique de France
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We investigate the existence of Lagrangian fibrations on the generalized Kummer varieties of Beauville. For a principally polarized abelian surface of Picard number one we find the following: The Kummer variety is birationally equivalent to another irreducible symplectic variety admitting a Lagrangian fibration, if and only if is a perfect square. And this is the case if and only if carries a divisor with vanishing Beauville-Bogomolov square.
Bao Qin Li, Enrique Villamor (2006)
Studia Mathematica
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A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space .
Giuseppe Lombardo (2006)
Bollettino dell'Unione Matematica Italiana
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We obtain coniugacy classes (with respect to a action) in the space of Hodge cycles in the middle cohomology of an Abelian variety of quaternionic type. The existence of such a class simplifies the study of the Hodge conjecture.
Anders S. Buch, Pierre-Emmanuel Chaput, Leonardo C. Mihalcea, Nicolas Perrin (2013)
Annales scientifiques de l'École Normale Supérieure
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The product of two Schubert classes in the quantum -theory ring of a homogeneous space is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on . We show that if is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to that take the marked points to general Schubert varieties and...
V. Uma (2013)
Colloquium Mathematicae
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We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in to R(T) ⊗ R(T), where R(T) denotes the representation ring of the torus T. We further apply our results to describe the multiplicative structure constants of where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure...
Behrouz Taji (2014)
Annales de l’institut Fourier
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In this paper we prove that for a nonsingular projective variety of dimension at most 4 and with non-negative Kodaira dimension, the Kodaira dimension of coherent subsheaves of is bounded from above by the Kodaira dimension of the variety. This implies the finiteness of the fundamental group for such an provided that has vanishing Kodaira dimension and non-trivial holomorphic Euler characteristic.
Do Duc Thai, Nguyen Huu Kien (2015)
Acta Arithmetica
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The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety , where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety
Valerie Cheng, Shelly Wismath (2008)
Discussiones Mathematicae - General Algebra and Applications
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Let τ be a type of algebras. A common measurement of the complexity of terms of type τ is the depth of a term. For k ≥ 1, an identity s ≈ t of type τ is said to be k-normal (with respect to this depth complexity measurement) if either s = t or both s and t have depth ≥ k. A variety is called k-normal if all its identities are k-normal. Taking k = 1 with respect to the usual depth valuation of terms gives the well-known property of normality of identities or varieties. For any variety...
М.Г. Амаглобели, В.Н. Ремесленников (2000)
Algebra i Logika
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Matt Kerr, Gregory Pearlstein (2014)
Annales de l’institut Fourier
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We give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups , , and .
Ekatarina Amerik, Marat Rovinsky, Antonius Van de Ven (1999)
Annales de l'institut Fourier
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The main result of this paper is as follows: let be smooth projective threefolds (over a field of characteristic zero) such that . If is not a projective space, then the degree of a morphism is bounded in terms of discrete invariants of and . Moreover, suppose that and are smooth projective -dimensional with cyclic Néron-Severi groups. If , then the degree of is bounded iff is not a flat variety. In particular, to prove our main theorem we show the non-existence of...
Arnaud Beauville (2014)
Journal de l’École polytechnique — Mathématiques
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For a smooth complex projective variety, the rank of the Néron-Severi group is bounded by the Hodge number . Varieties with have interesting properties, but are rather sparse, particularly in dimension . We discuss in this note a number of examples, in particular those constructed from curves with special Jacobians.
Tobias Heinrich (2005)
Annales Polonici Mathematici
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For an analytic variety V in ℂⁿ containing the origin which satisfies the local Phragmén-Lindelöf condition it is shown that for each real simple curve γ and each d ≥ 1 the limit variety satisfies the strong Phragmén-Lindelöf condition (SPL).
Tanya Bandman, Gerd Dethloff (1997)
Annales de l'institut Fourier
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First we find effective bounds for the number of dominant rational maps between two fixed smooth projective varieties with ample canonical bundles. The bounds are of the type , where , is the canonical bundle of and are some constants, depending only on . Then we show that for any variety there exist numbers and with the following properties: For any threefold of general type the number of dominant rational maps is bounded above by . ...