# Moscow Mathematical Journal

Volume 21, Issue 3, July–September 2021 pp. 639–652.

Toric Topology of the Grassmannian of Planes in $\mathbb{C}^5$ and the Del Pezzo Surface of Degree 5

**Authors**:
Hendrik Süß (1)

**Author institution:**(1) School of Mathematics, The University of Manchester, Alan Turing Building, Oxford Road, Manchester M13 9PL

**Summary: **

We determine the integral homology of the orbit space of a maximal compact torus action on the Grassmannian $\mathrm{Gr}(2,\mathbb C^5)$. This problem has been also studied by Buchstaber and Terzić via purely topological methods. Here, we propose an alternative approach via the well-known Geometric Invariant Theory of the algebraic torus action on this Grassmannian.

2020 Math. Subj. Class. Primary: 57S25; Secondary: 14L24, 53D20, 14J26

**Keywords:**Grassmannian, torus action, orbit space, Geometric Invariant Theory, del Pezzo surface.

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