Results 1 to 10 of about 535 (156)
Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials [PDF]
Comptes Rendus. Mathématique, 2023 The strata of the moduli spaces of Abelian differentials are non-homogenous spaces carrying natural bi-algebraic structures. Partly inspired by the case of homogenous spaces carrying bi-algebraic structures (such as torii, Abelian varieties and Shimura ...
Deroin, Bertrand, Matheus, Carlos
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Complete curves in the strata of differentials
Comptes Rendus. Mathématique, 2023 Gendron proved that the strata of holomorphic differentials with prescribed orders of zeros do not contain complete algebraic curves by applying the maximum modulus principle to saddle connections.
Chen, Dawei
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Brauer groups of moduli of hyperelliptic curves via cohomological invariants
Forum of Mathematics, Sigma, 2021 Using the theory of cohomological invariants for algebraic stacks, we compute the Brauer group of the moduli stack of hyperelliptic curves ${\mathcal {H}}_g$ over any field of characteristic $0$.
Andrea Di Lorenzo, Roberto Pirisi
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Hilbert-Mumford stability on algebraic stacks and applications to $\mathcal{G}$-bundles on curves [PDF]
Épijournal de Géométrie Algébrique, 2018 In these notes we reformulate the classical Hilbert-Mumford criterion for GIT stability in terms of algebraic stacks, this was independently done by Halpern-Leinster.
Jochen Heinloth
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Fibonacci, Golden Ratio, and Vector Bundles
Mathematics, 2021 There is a family of vector bundles over the moduli space of stable curves that, while first appearing in theoretical physics, has been an active topic of study for algebraic geometers since the 1990s. By computing the rank of the exceptional Lie algebra
Noah Giansiracusa
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Combinatorics of Bricard’s octahedra
Comptes Rendus. Mathématique, 2021 We re-prove the classification of motions of an octahedron — obtained by Bricard at the beginning of the XX century — by means of combinatorial objects satisfying some elementary rules.
Gallet, Matteo +3 more
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The eleventh cohomology group of $\overline {\mathcal {M}}_{g,n}$
Forum of Mathematics, Sigma, 2023 We prove that the rational cohomology group $H^{11}(\overline {\mathcal {M}}_{g,n})$ vanishes unless $g = 1$ and $n \geq 11$ . We show furthermore that $H^k(\overline {\mathcal {M}}_{g,n})$ is pure Hodge–Tate for all even ...
Samir Canning, Hannah Larson, Sam Payne
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Machine learning and algebraic approaches towards complete matter spectra in 4d F-theory
Journal of High Energy Physics, 2021 Motivated by engineering vector-like (Higgs) pairs in the spectrum of 4d F-theory compactifications, we combine machine learning and algebraic geometry techniques to analyze line bundle cohomologies on families of holomorphic curves. To quantify jumps of
Martin Bies +5 more
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MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY
Forum of Mathematics, Sigma, 2016 We study moduli spaces of rational weighted stable tropical curves, and their connections with Hassett spaces. Given a vector $w$ of weights, the moduli ...
RENZO CAVALIERI +3 more
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SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS
Forum of Mathematics, Pi, 2013 We study the postcritically finite maps within the moduli space of complex polynomial dynamical systems. We characterize rational curves in the moduli space containing an infinite number of postcritically finite maps, in terms of critical orbit relations,
MATTHEW BAKER, LAURA DE MARCO
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