Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0710.0122

A canonical bundle formular of projective Lagrangian fibrations

Daisuke Matsushita
View original source ↗Read source document ↗Export metadata ↓

Abstract

We classify singular fibres of a projective Lagrangian fibration over codimension one points. As an application, we obtain a canonical bundle formula for a projective Lagrangian fibration over a smooth manifold.

Explore related subjects

math.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Daisuke Matsushita. 2016-11-24. A canonical bundle formular of projective Lagrangian fibrations. https://arxiv.org/abs/0710.0122

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Algebra of global sections of $ψ$-bundles on $\bar{M}_{0,n}$

We consider the ${\mathbb Z}^n$-graded algebra of global sections of line bundles generated by the standard line bundles $L_1,\ldots,L_n$ on $\bar{M}_{0,n}$. We find a simple presentation of this algebra by generators and quadratic relations. As an application we prove that the moduli space $\bar{M}_{0,n}[ψ]$ of $ψ$-stable curves of genus $0$ is Cohen-Macaulay and normal, and the natural map $\bar{M}_{0,n}\to \bar{M}_{0,n}[ψ]$ is a rational resolution.

math.AG↗
arXiv2026

Minimum volumes of tropical rational functions

When a tropical rational function $φ$ on $\mathbb{R}^n$ is given, we can represent it as a tropical quotient $φ=f\oslash g$ with tropical polynomials $f$ and $g$. We develop the duality theorem for tropical rational functions to define a volume of the pair $(f, g)$. The first part concerns the case $n=1$. We show that when $n=1$, we can find a ``unique'' representation of $φ(x) \neq -\infty$ as $f(x)\oslash g(x)$ with the pair $(f, g)$ of minimum volume. However, when $n=2$, this is not true.

math.AG↗