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arXiv · 1709.08674

Numerical Polar calculus and cohomology of line bundles

Sandra Di Rocco·David Eklund·Chris Peterson
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Abstract

Let $L_1,\dots,L_s$ be line bundles on a smooth variety $X\subset \mathbb{P}^r$ and let $D_1,\dots,D_s$ be divisors on $X$ such that $D_i$ represents $L_i$. We give a probabilistic algorithm for computing the degree of intersections of polar classes which are in turn used for computing the Euler characteristic of linear combinations of $L_1,\dots,L_s$. The input consists of generators for the homogeneous ideals $I_X, I_{D_i} \subset \mathbb{C}[x_0,\ldots,x_r]$ defining $X$ and $D_i$.

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Sandra Di Rocco, David Eklund, Chris Peterson. 2017-09-25. Numerical Polar calculus and cohomology of line bundles. https://arxiv.org/abs/1709.08674

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