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Tensor complexes: multilinear free resolutions constructed from higher tensors

Christine Berkesch Zamaere, Daniel Erman, Manoj Kummini, Steven V. Sam (2013)

Journal of the European Mathematical Society

The most fundamental complexes of free modules over a commutative ring are the Koszul complex, which is constructed from a vector (i.e., a 1-tensor), and the Eagon-Northcott and Buchsbaum-Rim complexes, which are constructed from a matrix (i.e., a 2-tensor). The subject of this paper is a multilinear analogue of these complexes, which we construct from an arbitrary higher tensor. Our construction provides detailed new examples of minimal free resolutions, as well as a unifying view on a wide variety...

Tensor product theorem for Hitchin pairs – An algebraic approach

V. Balaji, A.J. Parameswaran (2011)

Annales de l’institut Fourier

We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields of characteristic zero and characteristic p , with p satisfying some natural bounds. We also prove the corresponding theorem for polystable Hitchin pairs.

Teorema de irreducibilidad para correspondencias algebraicas.

Eugenio Roanes (1980)

Revista Matemática Hispanoamericana

Sea T una correspondencia algebraica irreducible entre dos variedades proyectivas, V y V', sobre un cuerpo k algebraicamente cerrado y de característica cero. Sea W una subvariedad irreducible de V y W' = T{W} la transformada total de W en T. En [1] se estudia el problema de la conexión de W' y en [3] se estudia el problema de la irreducibilidad de la transformada total de W en correspondencias locales. La finalidad de este artículo es la de aprovechar los resultados de los dos trabajos citados,...

Teoría métrica de curvas semialgebráicas.

Lev Birbrair, Alexandre C. G. Fernandes (2000)

Revista Matemática Complutense

We present a complete bi-Lipschitz classification of germs of semialgebraic curves (semialgebraic sets of the dimension one). For this purpose we introduce the so-called Hölder Semicomplex, a bi-Lipschitz invariant. Hölder Semicomplex is the collection of all first exponents of Newton-Puiseux expansions, for all pairs of branches of a curve. We prove that two germs of curves are bi-Lipschitz equivalent if and only if the corresponding Hölder Semicomplexes are isomorphic. We also prove that any Hölder...

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