Author

Martin de Borbon

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Preprint Sep 2026

K\"ahler-Einstein cone metrics and parabolic bundles

Let $X$ be a compact K\"ahler manifold, let $D=\sum_iD_i$ be a simple normal crossing divisor, and fix $\beta_i\in(0,1)$. We introduce a parabolic structure $TX_*$ on $TX$, given along each $D_i$ by the filtration $0\subset TD_i\subset TX|_{D_i}$ with weight $w_i=1-\beta_i$ on the normal quotient. If $X\setminus D$ car...

Martin de Borbon · 0 citations

Preprint Oct 2026

Point-balanced arrangements in the real projective plane and the Hirzebruch property

A collection of $m \geq 2$ lines through the origin in $\mathbb{R}^2$ is balanced if the sum of the orthogonal projections onto these lines equals $m/2$ times the identity. A line arrangement in $\mathbb{RP}^2$, endowed with the round metric of curvature $1$, is point-balanced if the tangent lines at every vertex form...

Martin de Borbon · 0 citations