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Mathematics > Algebraic Geometry

arXiv:1807.06283 (math)
[Submitted on 17 Jul 2018 (v1), last revised 4 Apr 2019 (this version, v2)]

Title:Tropical Fano Schemes

Authors:Sara Lamboglia
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Abstract:We define a tropical version $\F_d(\trop X)$ of the Fano Scheme $\F_d(X)$ of a projective variety $X\subseteq \mathbb P^n$ and prove that $\F_d(\trop X)$ is the support of a polyhedral complex contained in $\trop \Grp(d,n)$. In general $\trop \F_d(X)\subseteq \F_d(\trop X)$ but we construct linear spaces $L$ such that $\trop \F_1(X)\subsetneq \F_1(\trop X)$ and show that for a toric variety $\trop \F_d(X)=\F_d(\trop X)$.
Comments: 16 pages, 3 figures. Version 2 contains generalised version of Theorems 2.3 and 4.2 where not just tropicalized lines are considered but any tropicalized linear space
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1807.06283 [math.AG]
  (or arXiv:1807.06283v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.06283

Submission history

From: Sara Lamboglia [view email]
[v1] Tue, 17 Jul 2018 08:54:58 UTC (528 KB)
[v2] Thu, 4 Apr 2019 13:40:09 UTC (21 KB)
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