Papers by Vasile Brînzănescu
arXiv (Cornell University), Jul 26, 2017
We clarify the relationship between the two most standard measurements of the order of contact of... more We clarify the relationship between the two most standard measurements of the order of contact of q-dimensional complex varieties with a real hypersurface, the Catlin and D'Angelo q-types, by showing that the former equals the generic value of the normalized order of contact measured along curves whose infimum is by definition the D'Angelo q-type. Contents 1. Introduction 1 2. Catlin and D'Angelo q-types 4 3. Proof of results 8 References 15 2020 Mathematics Subject Classification. Primary 32F18; 32T25; Secondary 32V35; 13H15. Key words and phrases. orders of contact, D'Angelo finite q-type, Catlin finite q-type, finite type domains in C n , pseudoconvexity.
Springer eBooks, 2014
In the paper [17], Sankaran gives a construction of some complex analytic manifolds, which are hi... more In the paper [17], Sankaran gives a construction of some complex analytic manifolds, which are higher-dimensional analogues of Inoue parabolic surfaces, by using methods of toric geometry (see also [9, 16]). Some higher-dimensional analogues of Kodaira surfaces are obtained as hypersurfaces in these Inoue manifolds. In this paper we construct another higher-dimensional analogues of primary Kodaira surfaces and we compute their invariants as the Hodge numbers.
At the beginning of our academic career we knew the name of the mathematician Marius Iosifescu, a... more At the beginning of our academic career we knew the name of the mathematician Marius Iosifescu, a renowned specialist, fellow of the Onicescu-Mihoc school in probability theory. Chains with complete connections, a remarkable contribution of the Romanian mathematical school to the theory of probability, cannot be presented without mentioning his results in the domain. We learned about the Markov chains from his booklet published in the seventies in Romanian language. In fact, this text become a classical one published by Editura Tehnicȃ, Bucharest, and then, as a revised expanded English translation in 1980, by John Wiley & Sons, Ltd. This edition was unanimously acclaimed and has a great success. Consequently, the book was republished in 2007 in the series Dover Books on Mathematics. We also have to mention the applications of the random systems with complete connections, which are extensions of the Markov chains, obtained by Marius Iosifescu in Probabilistic Number Theory, related to continued-fraction expansions. Another important achievement is a probabilistic framework for the Riemann hypothesis, concerning the complex zeros of the Zeta function. Marius Iosifescu is since forty years (1976) the director of the Center of Mathematical Statistics, the nowadays Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy. We participate since many years to the scientific events organized by this institution. We only mention the famous stochastic processes seminar from the eighties, where the Malliavin calculus was the main topic. At that time, in a so unfriendly social and political frame, which drastically affected the Center, Marius Iosifescu became our protector in a very discrete but efficient way. After 1989, as a member and later on, as vice-president of the Romanian Academy, Marius Iosifescu was deeply involved in the reconstruction of the institutes of the Academy, especially in the development of the mathematical institutes. He was for several decades the main editor of the journals "Revue Roumaine de Mathématiques Pures et Appliquées" and "Mathematical Reports", published by the Romanian Academy. This difficult and time continuous work is hard to be measured. Our institute, "Simion Stoilow" Institute of Mathematics of the Romanian Academy (abbreviated IMAR), receives his support in all its scientific activities, he helps us with his kind advice in the coordination of the research and management of IMAR. An European Laboratory Associated to CNRS, France, was founded at IMAR in 2007 and Marius Iosifescu was one of its initiators and always in the core of its activity. Actually, he coordinated a regular collaboration with France since 1992, when a series of French-Romanian conferences in Applied Mathematics started, organized each two years, alternatively in France and Romania. We take profit on Marius Iosifescu's long time scientific collaborations with renown research centers from other European
Lecture Notes in Mathematics, 1996
Nucleation and Atmospheric Aerosols, 2011
We describe some facts in physics which go up to the modern string theory and the related concept... more We describe some facts in physics which go up to the modern string theory and the related concepts in algebraic geometry. Then we present some recent results on moduli-spaces of vector bundles on non-Kähler Calabi-Yau 3-folds and their consequences for heterotic string theory.
International Mathematics Research Notices, Jul 3, 2014
The goal of this paper is the proof of the algebraic complete integrability of the Bloch-Iserles ... more The goal of this paper is the proof of the algebraic complete integrability of the Bloch-Iserles Hamiltonian system [5]. This result was conjectured in [4], based on its validity in certain special cases.
Journal of Geometry and Physics, May 1, 2015
We study rank-2 vector bundles on non-Kähler threefolds π : X → B, which are elliptic principal b... more We study rank-2 vector bundles on non-Kähler threefolds π : X → B, which are elliptic principal bundles with at least one non-zero Chern class over a complex surface B with no curves. In this case, we prove that every rank-2 irreducible vector bundle on X is a pull-back from B up to a twist by a line bundle. These 2-vector bundles are, via the Kobayashi-Hitchin correspondence, solutions of the Yang-Mills equations on the threefold X.
arXiv (Cornell University), Sep 2, 2003
In this paper, we study holomorphic rank-2 vector bundles on non-K\" ahler elliptic surfaces. Our... more In this paper, we study holomorphic rank-2 vector bundles on non-K\" ahler elliptic surfaces. Our main tool for analysing these bundles is of course the spectral cover. However, given the non-Kähler condition, the elliptic surfaces we are considering do not have sections and gerbes naturally arise in this context. The spectral construction presented in this paper is a modification of the Fourier-Mukai transform for elliptic fibrations without a section. After examining some of the properties of this Fourier-Mukai transform, we give a complete classification of vector bundles on these surfaces.
arXiv (Cornell University), Jun 11, 2003
In this paper, we study the moduli spaces M δ,c 2 of stable rank-2 vector bundles on non-Kähler e... more In this paper, we study the moduli spaces M δ,c 2 of stable rank-2 vector bundles on non-Kähler elliptic surfaces, thus giving a classification these bundles; in the case of Hopf and Kodaira surfaces, these moduli spaces admit the structure of an algebraically completely integrable Hamiltonian system.
arXiv (Cornell University), Jun 11, 2003
The existence problem for vector bundles on a smooth compact complex surface consists in determin... more The existence problem for vector bundles on a smooth compact complex surface consists in determining which topological complex vector bundles admit holomorphic structures. For projective surfaces, Schwarzenberger proved that a topological complex vector bundle admits a holomorphic (algebraic) structure if and only if its first Chern class belongs to the Neron-Severi group of the surface. In contrast, for non-projective surfaces there is only a necessary condition for the existence problem (the discriminant of the vector bundles must be positive) and the difficulty of the problem resides in the lack of a general method for constructing non-filtrable vector bundles. In this paper, we close the existence problem in the rank-2 case, by giving necessary and sufficient conditions for the existence of holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces.
Moduli Spaces and Vector Bundles
Manuscripta Mathematica, Dec 1, 1994
Journal of Geometry and Physics, Dec 1, 2006
Walczak formula is a very nice tool for understanding the geometry of a Riemannian manifold equip... more Walczak formula is a very nice tool for understanding the geometry of a Riemannian manifold equipped with two orthogonal complementary distributions. Svensson [14] has shown that this formula simplifies to a Bochner type formula when we are dealing with Kähler manifolds and holomorphic (integrable) distributions. We show in this paper that such results have a counterpart in Sasakian geometry. To this end, we build on a theory of (contact) holomorphicity on almost contact metric manifolds. Some other applications for (pseudo) harmonic morphisms on Sasaki manifolds are outlined.
International Journal of Mathematics, Dec 1, 2000
We introduce the class of pseudo-horizontally homothetic maps from a Riemann manifold to a Kähler... more We introduce the class of pseudo-horizontally homothetic maps from a Riemann manifold to a Kähler manifold, and we study some of their properties. For example, we prove that a pseudo-horizontally homothetic submersion is harmonic if and only if it has minimal fibres, and a pseudo-horizontally homothetic harmonic submersion pulls back complex submanifolds into minimal submanifolds.
Central European Journal of Mathematics, Mar 28, 2012
We survey some parts of the vast literature on vector bundles on Hirzebruch surfaces, focusing on... more We survey some parts of the vast literature on vector bundles on Hirzebruch surfaces, focusing on the rank-two case.
Mathematische Annalen, Dec 1, 1993
Annales de l'Institut Fourier, 2005
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Nagoya Mathematical Journal, 1999
We study moduli spaces M (c1, c2, d, r) of isomorphism classes of algebraic 2-vector bundles with... more We study moduli spaces M (c1, c2, d, r) of isomorphism classes of algebraic 2-vector bundles with fixed numerical invariants c1, c2, d, r over a ruled surface. These moduli spaces are independent of any ample line bundle on the surface. The main result gives necessary and sufficient conditions for the nonemptiness of the space M (c1, c2, d, r) and we apply this result to the moduli spaces ML(c1, c2) of stable bundles, where L is an ample line bundle on the ruled surface.
Lecture Notes in Mathematics, 1996
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Papers by Vasile Brînzănescu