Using Tropical Degenerations For Proving The Nonexistence Of Certain Nets

Details Using Tropical Degenerations For Proving The Nonexistence Of Certain Nets Using Tropical Degenerations For Proving The Nonexistence Of Certain Nets

2011-07-27

arxiv.org/abs/1107.5530v3

Mathematics

Algebraic Geometry

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Scientific paper

A net is a special configuration of lines and points in the projective plane.
There are certain restrictions on the number of its lines and points. We proved
that there cannot be any (4,4) nets in $\mathbb{C}P^2$. In order to show this,
we use tropical algebraic geometry. We tropicalize the hypothetical net and
show that there cannot be such a configuration in $\mathbb{C}P^2$.

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