Relevant bibliographies by topics / Hassett's moduli spaces

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Academic literature on the topic 'Hassett's moduli spaces'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Hassett's moduli spaces"

1

Massarenti, Alex, and Massimiliano Mella. "On the automorphisms of Hassett’s moduli spaces." Transactions of the American Mathematical Society 369, no. 12 (May 30, 2017): 8879–902. http://dx.doi.org/10.1090/tran/6966.

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2

Smyth, David Ishii. "Modular compactifications of the space of pointed elliptic curves II." Compositio Mathematica 147, no. 6 (August 30, 2011): 1843–84. http://dx.doi.org/10.1112/s0010437x11005549.

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AbstractWe prove that the moduli spaces of n-pointed m-stable curves introduced in our previous paper have projective coarse moduli. We use the resulting spaces to run an analogue of Hassett’s log minimal model program for $\overline {M}_{1,n}$.
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3

Cerbu, Alois, Steffen Marcus, Luke Peilen, Dhruv Ranganathan, and Andrew Salmon. "Topology of tropical moduli of weighted stable curves." Advances in Geometry 20, no. 4 (October 27, 2020): 445–62. http://dx.doi.org/10.1515/advgeom-2019-0034.

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AbstractThe moduli space Δg,w of tropical w-weighted stable curves of volume 1 is naturally identified with the dual complex of the divisor of singular curves in Hassett’s spaces of w-weighted stable curves. If at least two of the weights are 1, we prove that Δ0, w is homotopic to a wedge sum of spheres, possibly of varying dimensions. Under additional natural hypotheses on the weight vector, we establish explicit formulas for the Betti numbers of the spaces. We exhibit infinite families of weights for which the space Δ0,w is disconnected and for which the fundamental group of Δ0,w has torsion. In the latter case, the universal cover is shown to have a natural modular interpretation. This places the weighted variant of the space in stark contrast to the heavy/light cases studied previously by Vogtmann and Cavalieri–Hampe–Markwig–Ranganathan. Finally, we prove a structural result relating the spaces of weighted stable curves in genus 0 and 1, and leverage this to extend several of our genus 0 results to the spaces Δ1,w.
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4

Alper, Jarod, Maksym Fedorchuk, and David Ishii Smyth. "Second flip in the Hassett–Keel program: existence of good moduli spaces." Compositio Mathematica 153, no. 8 (May 15, 2017): 1584–609. http://dx.doi.org/10.1112/s0010437x16008289.

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We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the Keel–Mori theorem, which guarantees the existence of a coarse moduli space for a separated Deligne–Mumford stack. We apply this result to prove that the moduli stacks $\overline{{\mathcal{M}}}_{g,n}(\unicode[STIX]{x1D6FC})$ parameterizing $\unicode[STIX]{x1D6FC}$-stable curves introduced in [J. Alper et al., Second flip in the Hassett–Keel program: a local description, Compositio Math. 153 (2017), 1547–1583] admit good moduli spaces.
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5

Laza, Radu, and Kieran O’Grady. "Birational geometry of the moduli space of quartic surfaces." Compositio Mathematica 155, no. 9 (August 2, 2019): 1655–710. http://dx.doi.org/10.1112/s0010437x19007516.

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By work of Looijenga and others, one understands the relationship between Geometric Invariant Theory (GIT) and Baily–Borel compactifications for the moduli spaces of degree-$2$ $K3$ surfaces, cubic fourfolds, and a few other related examples. The similar-looking cases of degree-$4$ $K3$ surfaces and double Eisenbud–Popescu–Walter (EPW) sextics turn out to be much more complicated for arithmetic reasons. In this paper, we refine work of Looijenga in order to handle these cases. Specifically, in analogy with the so-called Hassett–Keel program for the moduli space of curves, we study the variation of log canonical models for locally symmetric varieties of Type IV associated to $D$-lattices. In particular, for the $19$-dimensional case, we conjecturally obtain a continuous one-parameter interpolation between the GIT and Baily–Borel compactifications for the moduli of degree-$4$ $K3$ surfaces. The analogous $18$-dimensional case, which corresponds to hyperelliptic degree-$4$ $K3$ surfaces, can be verified by means of Variation of Geometric Invariant Theory (VGIT) quotients.
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6

Ballard, Matthew, David Favero, and Ludmil Katzarkov. "Variation of geometric invariant theory quotients and derived categories." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 746 (January 1, 2019): 235–303. http://dx.doi.org/10.1515/crelle-2015-0096.

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Abstract We study the relationship between derived categories of factorizations on gauged Landau–Ginzburg models related by variations of the linearization in Geometric Invariant Theory. Under assumptions on the variation, we show the derived categories are comparable by semi-orthogonal decompositions and we completely describe all components appearing in these semi-orthogonal decompositions. We show how this general framework encompasses many well-known semi-orthogonal decompositions. We then proceed to give applications of this complete description. In this setting, we verify a question posed by Kawamata: we show that D-equivalence and K-equivalence coincide for such variations. The results are applied to obtain a simple inductive description of derived categories of coherent sheaves on projective toric Deligne–Mumford stacks. This recovers Kawamata’s theorem that all projective toric Deligne–Mumford stacks have full exceptional collections. Using similar methods, we prove that the Hassett moduli spaces of stable symmetrically-weighted rational curves also possess full exceptional collections. As a final application, we show how our results recover and extend Orlov’s σ-model/Landau–Ginzburg model correspondence.
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7

CAVALIERI, RENZO, SIMON HAMPE, HANNAH MARKWIG, and DHRUV RANGANATHAN. "MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY." Forum of Mathematics, Sigma 4 (2016). http://dx.doi.org/10.1017/fms.2016.7.

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We study moduli spaces of rational weighted stable tropical curves, and their connections with Hassett spaces. Given a vector $w$ of weights, the moduli space of tropical $w$-stable curves can be given the structure of a balanced fan if and only if $w$ has only heavy and light entries. In this case, the tropical moduli space can be expressed as the Bergman fan of an explicit graphic matroid. The tropical moduli space can be realized as a geometric tropicalization, and as a Berkovich skeleton, its algebraic counterpart. This builds on previous work of Tevelev, Gibney and Maclagan, and Abramovich, Caporaso and Payne. Finally, we construct the moduli spaces of heavy/light weighted tropical curves as fibre products of unweighted spaces, and explore parallels with the algebraic world.
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8

Ascher, Kenneth, Kristin DeVleming, and Yuchen Liu. "K-stability and birational models of moduli of quartic K3 surfaces." Inventiones mathematicae, November 27, 2022. http://dx.doi.org/10.1007/s00222-022-01170-5.

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AbstractWe show that the K-moduli spaces of log Fano pairs $$({\mathbb {P}}^3, cS)$$ ( P 3 , c S ) where S is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily–Borel compactification of moduli of quartic K3 surfaces as c varies in the interval (0, 1). We completely describe the wall crossings of these K-moduli spaces. As the main application, we verify Laza–O’Grady’s prediction on the Hassett–Keel–Looijenga program for quartic K3 surfaces. We also obtain the K-moduli compactification of quartic double solids, and classify all Gorenstein canonical Fano degenerations of $${\mathbb {P}}^3$$ P 3 .
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