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Gale duality for complete intersections

Frédéric Bihan, Frank Sottile (2008)

Annales de l’institut Fourier

We show that every complete intersection defined by Laurent polynomials in an algebraic torus is isomorphic to a complete intersection defined by master functions in the complement of a hyperplane arrangement, and vice versa. We call systems defining such isomorphic schemes Gale dual systems because the exponents of the monomials in the polynomials annihilate the weights of the master functions. We use Gale duality to give a Kouchnirenko theorem for the number of solutions to a system of master...

Galois covers between K 3 surfaces

Gang Xiao (1996)

Annales de l'institut Fourier

We give a classification of finite group actions on a K 3 surface giving rise to K 3 quotients, from the point of view of their fixed points. It is shown that except two cases, each such group gives rise to a unique type of fixed point set.

Geometric and categorical nonabelian duality in complex geometry

Siegmund Kosarew (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The Leitmotiv of this work is to find suitable notions of dual varieties in a general sense. We develop the basic elements of a duality theory for varieties and complex spaces, by adopting a geometric and a categorical point of view. One main feature is to prove a biduality property for each notion which is achieved in most cases.

Geometry of arithmetically Gorenstein curves in P4.

Robin Hartshorne (2004)

Collectanea Mathematica

We characterize the postulation character of arithmetically Gorenstein curves in P4. We give conditions under which the curve can be realized in the form mH - K on some ACM surface. Finally, we complement a theorem by Watanabe by showing that any general arithmetically Gorenstein curve in P4 with arbitrary fixed postulation character can be obtained from a line by a series of ascending complete-intersection biliaisons.

Geometry of the genus 9 Fano 4-folds

Frédéric Han (2010)

Annales de l’institut Fourier

We study the geometry of a general Fano variety of dimension four, genus nine, and Picard number one. We compute its Chow ring and give an explicit description of its variety of lines. We apply these results to study the geometry of non quadratically normal varieties of dimension three in a five dimensional projective space.

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