Algebraic equations and convex bodies Export

@article{citeulike:3838857, abstract = {The well-known Bernstein-Kushnirenko theorem from the theory of Newton polyhedra relates algebraic geometry and the theory of mixed volumes. Recently the authors have found a far-reaching generalization of this theorem to generic systems of algebraic equations on any quasi-projective variety. In the present note we review these results and their applications to algebraic geometry and convex geometry.}, archivePrefix = {arXiv}, author = {Kaveh, Kiumars and Khovanskii, A. G.}, citeulike-article-id = {3838857}, citeulike-linkout-0 = {http://arxiv.org/abs/0812.4688}, citeulike-linkout-1 = {http://arxiv.org/pdf/0812.4688}, day = {26}, eprint = {0812.4688}, keywords = {algebraic\_geometry, complex\_analysis, root\_location, tropical\_geometry}, month = {Dec}, posted-at = {2008-12-31 07:38:36}, priority = {4}, title = {Algebraic equations and convex bodies}, url = {http://arxiv.org/abs/0812.4688}, year = {2008} }

TY - JOUR ID - citeulike:3838857 L3 - citeulike-article-id:3838857 N2 - The well-known Bernstein-Kushnirenko theorem from the theory of Newton polyhedra relates algebraic geometry and the theory of mixed volumes. Recently the authors have found a far-reaching generalization of this theorem to generic systems of algebraic equations on any quasi-projective variety. In the present note we review these results and their applications to algebraic geometry and convex geometry. TI - Algebraic equations and convex bodies KW - algebraic_geometry KW - complex_analysis KW - root_location KW - tropical_geometry AU - Kaveh, Kiumars AU - Khovanskii, AG PY - 2008/Dec/26/ UR - http://arxiv.org/abs/0812.4688 ER -