43 research outputs found
Elimination Theory for Tropical Varieties
Tropical algebraic geometry offers new tools for elimination theory and
implicitization. We determine the tropicalization of the image of a subvariety
of an algebraic torus under any homomorphism from that torus to another torus.Comment: 19 page
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Toric Geometry
Toric Geometry plays a major role where a wide variety of mathematical fields intersect, such as algebraic and symplectic geometry, algebraic groups, and combinatorics. The main feature of this workshop was to bring people from these area together to learn about mutual, possibly up till now unnoticed similarities in their respective research
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Cohomological Aspects of Hamiltonian Group Actions and Toric Varieties
[no abstract available
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Toric Geometry
Toric geometry is a subfield of algebraic geometry with rich
interactions with geometric combinatorics, and many other fields of
mathematics. This workshop brought together a broad range of mathematicians interested in toric matters, and their generalizations and applications
Mirror symmetry and tropical geometry
Using tropical geometry we propose a mirror construction for monomial
degenerations of Calabi-Yau varieties in toric Fano varieties. The construction
reproduces the mirror constructions by Batyrev for Calabi-Yau hypersurfaces and
by Batyrev and Borisov for Calabi-Yau complete intersections. We apply the
construction to Pfaffian examples and recover the mirror given by Rodland for
the degree 14 Calabi-Yau threefold in PP^6 defined by the Pfaffians of a
general linear 7x7 skew-symmetric matrix.
We provide the necessary background knowledge entering into the tropical
mirror construction such as toric geometry, Groebner bases, tropical geometry,
Hilbert schemes and deformations. The tropical approach yields an algorithm
which we illustrate in a series of explicit examples.Comment: 540 pages, 46 figure