Compact moduli of plane curves

By P. Hacking. 2003

129 citations recorded by the source corpus.

We construct a compactication Md of the moduli space of plane curves of degreed. We regard a plane curveC P 2 as a surface-divisor pair (P 2 ;C) and dene Md as a moduli space of pairs (X;D) where X is a degeneration of the plane. We show that, if d is not divisible by 3, the stackMd is smooth and the degenerate surfaces X can be described explicitly. MSC2000: 14H10, 14J10, 14E30.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/557e81278b4f99554744e491dddf158bb2452750

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

The moduli space of cubic fourfolds via the period map (2007, background): “ cubic fourfold are h4,0 = h0,4 = 0, h3,1 = h1,3 = 1, and h2,2 = 21. Thus, the classifying space of the Hodge structures for cubic fourfolds is a 20-dimensional Type IV bounded symmetric domain D∼=SO0(20,2)/SO(20)×SO(2). We regard Das the space of lines in Λ0 ⊗Csatisfying the two Riemann-Hodge bilin”
Higher-dimensional analogues of stable curves (2006, methodology): “ corresponding to arbitrarydimensional polarized varieties with canonical singularities was proved by Viehweg [48] by using methods of Geometric Invariant Theory. A ﬂoating coeﬃcient version. Hacking [22] constructed a moduli space for the stable pairs (P2,(3/d+ ǫ)B), where Bis a plane curve of degr”
Stable pair, tropical, and log canonical compactifications of moduli spaces of del Pezzo surfaces (2007, background): “(4) Following the philosophy of [22] and [2] we believe that Y n lc (n≥ 6) itself has a natural functorial meaning—namely the moduli space of stable pairs (S, cB) where the coefficient c is minimal.”
MODULI OF WEIGHTED STABLE MAPS AND THEIR GRAVITATIONAL DESCENDANTS (2006, background): “Hacking studied surface pairs (X, (3/d+ )D) with weights in [15], and the moduli compactifications of toric and abelian pairs [3] can be interpreted as moduli spaces of pairs (X, ∆ + D), respectively (X, D) with weights.”
Theta functions on varieties with effective anti-canonical class (2016, methodology): “ → X j induces an isomorphism Γ(X j,O X j ) −→R j = Γ(X◦ j,O X◦ j ). In particular, X j = Spec(R j) and R j is freely generated by the θj m. Intheproofwe used thefollowingtechnical lemma generalizing [Hk], Lemma A.3. Lemma 3.18. Let X→Sbe a ﬂat family of schemes of pure dimension nsuch that each ﬁbr”
Log minimal model program for the moduli space of stable curves of genus three (2007, methodology): “Hacking gave an alternate compactification of the moduli space of plane curves of degree d [3] by employing a method similar to [5] but allowing worse singularities.”
Compactification of the moduli space of hyperplane arrangements (2005, background): “[Hacking04] P.Hacking,Com pact m oduliofplane curves,Duke M ath.”
Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces (2009, background): “een shown in [HK04] that Viehweg families give rise to a good moduli space. The purpose of this article is to address the case of Koll´ar families. While this question has been considered before (cf. [Hac04]), the solution we propose is perhaps more natural than previous approaches, and has implicat”