An SL(3, C)-equivariant smooth compactification of moduli space of rational quartic plane curves

초록

Let Rd be the space of stable sheaves F which satisfy the Hilbert polynomial chi(F(m)) = dm + 1 and are supported on rational curves in the projective plane P2. Then R1 (resp. R2) is isomorphic to P2 (resp. P5). In addition, R3 is well-known to be a P6-bundle over P2. In particular, Rd is smooth for d <= 3. However, for d >= 4, in general, the space Rd is no longer smooth because of the complexity of boundary curves. In this paper, we obtained an SL(3, C)-equivariant smooth resolution of R4 for d = 4, which is a P5-bundle over a blowup of a Kronecker modules space. (c) 2024 Elsevier Inc. All rights reserved.

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