Tropical Homology
Copyright policy )Tropical Homology
Given a tropical variety X and two non-negative integers p and q we define homology group $H_{p,q}(X)$. We show that if X is a smooth tropical variety that can be represented as the tropical limit of a 1-parameter family of complex projective varieties, then $\dim H_{p,q}(X)$ coincides with the Hodge number $h^{p,q}$ of a general member of the family.
42 PAGES, 1 figure, introduction expanded and references added, publication status added
- Sorbonne University France
- PSL Research University France
- University of Vienna Austria
- École Normale Supérieure Burundi
- Institut de Mathématiques de Jussieu France
monodromy, [MATH] Mathematics [math], Geometric aspects of tropical varieties, smooth tropical variety, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), complex projective variety, Mathematics - Algebraic Geometry, hyperplane arrangements, Transcendental methods, Hodge theory (algebro-geometric aspects), Structure of families (Picard-Lefschetz, monodromy, etc.), FOS: Mathematics, Hodge structure, Algebraic Geometry (math.AG)
monodromy, [MATH] Mathematics [math], Geometric aspects of tropical varieties, smooth tropical variety, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), complex projective variety, Mathematics - Algebraic Geometry, hyperplane arrangements, Transcendental methods, Hodge theory (algebro-geometric aspects), Structure of families (Picard-Lefschetz, monodromy, etc.), FOS: Mathematics, Hodge structure, Algebraic Geometry (math.AG)
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