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Semi-group conditions for affine algebraic plane curves with more than one place at infinity.

Penelope G. Wightwick (2007)

Revista Matemática Complutense

An interesting and open question is the classification of affine algebraic plane curves. Abhyankar and Moh (1977) completely described the possible links at infinity for those curves where the link has just one component, a knot. Such curves are said to have one place at infinity. The Abhyankar-Moh result has been of great assistance in classifying those polynomials which define a connected curve with one place at infinity. This paper provides a new proof of the Abhyankar-Moh result which is then...

Semi-infinite cohomology and superconformal algebras

Elena Poletaeva (2001)

Annales de l’institut Fourier

We describe representations of certain superconformal algebras in the semi-infinite Weil complex related to the loop algebra of a complex finite-dimensional Lie algebra and in the semi-infinite cohomology. We show that in the case where the Lie algebra is endowed with a non-degenerate invariant symmetric bilinear form, the relative semi-infinite cohomology of the loop algebra has a structure, which is analogous to the classical structure of the de Rham cohomology in Kähler...

Semi-monotone sets

Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov (2013)

Journal of the European Mathematical Society

A coordinate cone in n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of n , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone...

Semi-simple Carrousels and the Monodromy

David B. Massey (2006)

Annales de l’institut Fourier

Let 𝒰 be an open neighborhood of the origin in n + 1 and let f : ( 𝒰 , 0 ) ( , 0 ) be complex analytic. Let z 0 be a generic linear form on n + 1 . If the relative polar curve Γ f , z 0 1 at the origin is irreducible and the intersection number ( Γ f , z 0 1 · V ( f ) ) 0 is prime, then there are severe restrictions on the possible degree n cohomology of the Milnor fiber at the origin. We also obtain some interesting, weaker, results when ( Γ f , z 0 1 · V ( f ) ) 0 is not prime.

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