Proves finiteness of reducible fibers over degree-d algebraic points for curve coverings over number fields, with a consequence for high-degree indecomposable rational functions to P1.
267 of Grundlehren Der Mathematischen Wissenschaften
7 Pith papers cite this work. Polarity classification is still indexing.
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The authors define divisible weighted projective spaces, give sharp bounds for minimal-degree non-degenerate subvarieties therein, and develop a theory of weighted determinantal scrolls that achieve minimal degree while satisfying weighted N_p properties tied to regularity notions.
Unified description of gaps G(Q) and Weierstrass semigroup H(Q) at totally ramified degree-one places in linearized function fields, with explicit generators and symmetry condition.
Explicit descriptions of Weierstrass semigroups and gaps at totally ramified places on Kummer extensions, plus symmetry conditions and minimal generators, with applications to GGS and BM curves.
For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
Rigidity is established for isotropic harmonic maps from the 2-torus to CP space arising from complete linear systems, and for broader holomorphic embeddings lacking hyperosculation points when Fubini-Study pullbacks satisfy an extra condition.
Stable pairs yield small Q-factorial modifications of Quot schemes on curves, making their large-degree fibers Mori dream spaces and the determinant morphism a Mori dream morphism.
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Hilbert irreducibility for algebraic points
Proves finiteness of reducible fibers over degree-d algebraic points for curve coverings over number fields, with a consequence for high-degree indecomposable rational functions to P1.
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The authors define divisible weighted projective spaces, give sharp bounds for minimal-degree non-degenerate subvarieties therein, and develop a theory of weighted determinantal scrolls that achieve minimal degree while satisfying weighted N_p properties tied to regularity notions.
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Weierstrass semigroups at totally ramified places of degree one on linearized function fields
Unified description of gaps G(Q) and Weierstrass semigroup H(Q) at totally ramified degree-one places in linearized function fields, with explicit generators and symmetry condition.
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Explicit descriptions of Weierstrass semigroups and gaps at totally ramified places on Kummer extensions, plus symmetry conditions and minimal generators, with applications to GGS and BM curves.
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Gaiotto Loci and the Nilpotent Cone for $\mathrm{Sp}_{2n}(\mathbb C)$
For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
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Birational Geometry of Quot Schemes on smooth projective curves via Stable Pairs
Stable pairs yield small Q-factorial modifications of Quot schemes on curves, making their large-degree fibers Mori dream spaces and the determinant morphism a Mori dream morphism.