# Gale duality for complete intersections

Frédéric Bihan^{[1]}; Frank Sottile^{[2]}

- [1] Université de Savoie Laboratoire de Mathématiques 73376 Le Bourget-du-Lac Cedex (France)
- [2] Department of Mathematics Texas A&M University College Station Texas 77843 (USA)

Annales de l’institut Fourier (2008)

- Volume: 58, Issue: 3, page 877-891
- ISSN: 0373-0956

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topBihan, Frédéric, and Sottile, Frank. "Gale duality for complete intersections." Annales de l’institut Fourier 58.3 (2008): 877-891. <http://eudml.org/doc/10337>.

@article{Bihan2008,

abstract = {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 functions and to compute some topological invariants of master function complete intersections.},

affiliation = {Université de Savoie Laboratoire de Mathématiques 73376 Le Bourget-du-Lac Cedex (France); Department of Mathematics Texas A&M University College Station Texas 77843 (USA)},

author = {Bihan, Frédéric, Sottile, Frank},

journal = {Annales de l’institut Fourier},

keywords = {Sparse polynomial system; hyperplane arrangement; master function; fewnomial; complete intersection; sparse polynomial systems; hyperplane arrangements; master functions; fewnomials; complete intersections},

language = {eng},

number = {3},

pages = {877-891},

publisher = {Association des Annales de l’institut Fourier},

title = {Gale duality for complete intersections},

url = {http://eudml.org/doc/10337},

volume = {58},

year = {2008},

}

TY - JOUR

AU - Bihan, Frédéric

AU - Sottile, Frank

TI - Gale duality for complete intersections

JO - Annales de l’institut Fourier

PY - 2008

PB - Association des Annales de l’institut Fourier

VL - 58

IS - 3

SP - 877

EP - 891

AB - 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 functions and to compute some topological invariants of master function complete intersections.

LA - eng

KW - Sparse polynomial system; hyperplane arrangement; master function; fewnomial; complete intersection; sparse polynomial systems; hyperplane arrangements; master functions; fewnomials; complete intersections

UR - http://eudml.org/doc/10337

ER -

## References

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