Mathematics > Algebraic Geometry
arXiv:2509.14812 (math)
[Submitted on 18 Sep 2025 (v1), last revised 23 Jun 2026 (this version, v5)]
Abstract:Using orbifold Hilbert schemes, we compactify all two-dimensional Hitchin systems corresponding to types A0-tilde, D4-tilde, E6-tilde, E7-tilde, and E8-tilde, thereby obtaining four rational elliptic surfaces with C*-actions. Their singular fibers and relative minimal models are listed in the main table. A particularly interesting point is that we found they can all be obtained by performing a finite number of blow-ups on the second Hirzebruch surface. To this end, we prove that Hilbert schemes of orbifold surfaces are connected smooth projective schemes under suitable conditions, and we use the Hilbert-Chow morphism to construct the minimal resolutions of the coarse moduli spaces.
Submission history
From: Yonghong Huang [view email]
[v1]
Thu, 18 Sep 2025 10:13:03 UTC (46 KB)
[v2]
Sun, 19 Oct 2025 02:53:38 UTC (47 KB)
[v3]
Wed, 25 Mar 2026 14:51:17 UTC (49 KB)
[v4]
Thu, 26 Mar 2026 16:33:21 UTC (49 KB)
[v5]
Tue, 23 Jun 2026 01:07:02 UTC (49 KB)
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