A tropical approach to enumerative geometry
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Publication:5481306
DOI10.1090/S1061-0022-06-00908-3zbMath1100.14046MaRDI QIDQ5481306
Publication date: 9 August 2006
Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)
Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Real algebraic sets (14P05) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Families, moduli of curves (analytic) (14H15)
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Refined count for rational tropical curves in arbitrary dimension, Enumeration of algebraic and tropical singular hypersurfaces, Secondary fans and tropical Severi varieties, Patchworking singular algebraic curves. I, Patchworking singular algebraic curves. II, On the singular locus of a plane projection of a complete intersection, Logarithmic asymptotics of the genus zero {G}romov-{W}itten invariants of the blown up plane, Enumeration of rational curves with cross-ratio constraints, Morsifications of real plane curve singularities, Tropical Severi varieties, Tropicalization of 1-tacnodal curves on toric surfaces, Real log curves in toric varieties, tropical curves, and log Welschinger invariants, Newton polygons and curve gonalities, Tropicalization of the moduli space of stable maps, Genus 0 logarithmic and tropical fixed‐domain counts for Hirzebruch surfaces, Tropical curves in abelian surfaces II: Enumeration of curves in linear systems, Floor diagrams and enumerative invariants of line bundles over an elliptic curve, An imaginary refined count for some real rational curves, Tropical vertex and real enumerative geometry, A note on the Severi problem for toric surfaces, Enumeration of complex and real surfaces via tropical geometry, Supertropical algebra, Tropical curves with a singularity in a fixed point, Characteristic classes of affine varieties and Plücker formulas for affine morphisms, Embeddings and immersions of tropical curves, Real algebraic curves with large finite number of real points, Examples of tropical-to-Lagrangian correspondence, Tropical noetherity and Gröbner bases, Real algebraic curves of bidegree (5,5) on the quadric ellipsoid
Cites Work
- La methode d'Horace pour l'interpolation à plusieurs variables
- Real plane algebraic curves with prescribed singularities
- Gluing of singular and critical points
- Counting plane curves of any genus
- Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry.
- Counting curves via lattice paths in polygons
- Amoebas, Monge-Ampère measures, and triangulations of the Newton polytope
- Viro theorem and topology of real and complex combinatorial hypersurfaces.
- Real algebraic curves, the moment map and amoebas
- Singular points and limit cycles of planar polynomial vector fields
- Laurent determinants and arrangements of hyperplane amoebas
- Patchworking singular algebraic curves. II
- Ideals Associated to Deformations of Singular Plane Curves
- Equisingular Deformations of Plane Algebroid Curves
- Enumerating curves on rational surfaces: the rational fibration method
- Surjectivity of the resultant map: a solution to the inverse bezout problem
- Stratification des espaces de polynômes de Laurent et la structure de leurs amibes
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