All Questions
Tagged with tropical-geometry toric-varieties
7 questions
2
votes
0
answers
104
views
Kouchnirenko's theorem for non-generic polynomials
In Polyèdres de Newton et nombres de Milnor (Theorem 1.18), Kouchnirenko proved that given Laurent polynomials $f_1, \dotsc, f_k$ in $k$ variables, the number of isolated solutions is less than or ...
- 315
2
votes
0
answers
103
views
Amoeba for a K3 surface in $\mathbb {CP}^3$
Let $X=X_\Delta$ be the toric variety associated to a reflexive polyhedron $\Delta$.
Consider a Calabi-Yau hypersurface $Y\subset X$, and the image of $Y$ under the moment map $\mu:X\to \Delta$ has ...
- 2,789
2
votes
0
answers
205
views
Local toric varieties and tropicalization
Let $K$ be a valued field, and consider the ring $R=K((x_1,\dots,x_m))$ of formal Laurent series. This is "the germ of the torus at $0$". Is there a theory of "local toric varieties" where $R$ ...
- 2,788
6
votes
1
answer
1k
views
Is there any structure theorem for piecewise linear functions?
I was wondering if such statements are known like "any piecewise linear function from $\mathbb{R}^d \rightarrow \mathbb{R}$ can be written as $\sum_{i=1}^k \alpha_i (\text{ some $2$ piece linear ...
- 2,246
3
votes
1
answer
529
views
How to recover toric invariants tropically?
My excuses in advance in case my question is too vague (which is mainly due to the fact that I'm not really familiar with tropical/toric geometry, but at least I still believe that the content of the ...
- 2,029
3
votes
1
answer
614
views
Hypersurfaces in Toric Varieties, Help understand a proof from Mikhalkin's paper
Hello,
in G. Mikhalkin's Papaer "DECOMPOSITION INTO PAIRS-OF-PANTS FOR
COMPLEX ALGEBRAIC HYPERSURFACES":
http://arxiv.org/pdf/math/0205011.pdf
There is a lemma about the relation between intersection ...
- 1,893
4
votes
1
answer
719
views
Intersection of curves on projective toric surface and some enumerative questions
Reading on the tropical approach to enumerative geometry I have come across the claim:
given a projective toric surface from a polygon P, we can consider a tautological bundle of algebraic / ...
- 1,893