Four counterexamples to converses of geometric-finiteness implications in round convex projective geometry are constructed using 4-dimensional domains invariant under the irreducible representation of SL₂(ℝ).
Higher Du Bois and higher rational singularities
11 Pith papers cite this work, alongside 1,573 external citations. Polarity classification is still indexing.
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Hilbert functions of Koszul maps turn empirical chamber-wise polynomial formulae for line bundle cohomology on CICY threefolds into explicit analytic or finite-box certified statements.
For primes N and p with N ≡ 1 mod p, the rank r of Mazur's Eisenstein Hecke algebra equals one plus the vanishing order of a mod-p zeta element interpolating L-values at -1 when r is 2 or 3, with a uniform extension to level N² and partial results for higher ranks.
Proves existence of positive-density hypersurfaces over finite fields intersecting a reduced equidimensional quasiprojective scheme X such that multiplicity e_P is preserved at all closed points P of the intersection.
K-theory rings of toric and flag varieties are realized as quotients of group algebras from linear families of virtual polytopes, yielding natural relations and descriptions of structure sheaf classes, including in the T-equivariant case.
Matrix representations for implicitization of rational hypersurfaces via syzygies on coefficient ideals in the Cox ring, removing the LCI-at-base-points requirement for surfaces.
A β-deformed version of motivic Segre classes of Schubert cells is constructed via the connective formal group law, with rational representatives via lattice models and structure constants via Knutson-Tao puzzles proven using quantum group intertwiners for d=1.
Introduces quasi-rational singularities and proves an isolated singularity is rational precisely when it is quasi-rational, Du Bois, and certain local mixed Hodge numbers vanish.
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
Proves inductive relationships and supplies inner and outer bounds on the multigraded regularity regions of the complete flag variety under the Plücker embedding.
Sufficient criteria are given for ambiskew polynomial rings to be differentially smooth.
citing papers explorer
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On 4-dimensional convex projective domains invariant by a lattice of $\mathrm{SL}_2 (\mathbb{R})$
Four counterexamples to converses of geometric-finiteness implications in round convex projective geometry are constructed using 4-dimensional domains invariant under the irreducible representation of SL₂(ℝ).
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Hilbert Functions and Line Bundle Cohomology on CICY Threefolds
Hilbert functions of Koszul maps turn empirical chamber-wise polynomial formulae for line bundle cohomology on CICY threefolds into explicit analytic or finite-box certified statements.
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A new perspective on the rank of Mazur's Eisenstein Hecke algebra
For primes N and p with N ≡ 1 mod p, the rank r of Mazur's Eisenstein Hecke algebra equals one plus the vanishing order of a mod-p zeta element interpolating L-values at -1 when r is 2 or 3, with a uniform extension to level N² and partial results for higher ranks.
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Bertini theorems for Hilbert-Samuel multiplicity over finite fields
Proves existence of positive-density hypersurfaces over finite fields intersecting a reduced equidimensional quasiprojective scheme X such that multiplicity e_P is preserved at all closed points P of the intersection.
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Polyhedral models for K-theory of toric and flag varieties
K-theory rings of toric and flag varieties are realized as quotients of group algebras from linear families of virtual polytopes, yielding natural relations and descriptions of structure sheaf classes, including in the T-equivariant case.
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Implicitization of rational hypersurfaces by syzygies with respect to coefficient ideals
Matrix representations for implicitization of rational hypersurfaces via syzygies on coefficient ideals in the Cox ring, removing the LCI-at-base-points requirement for surfaces.
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Motivic Segre classes of Schubert cells and the connective formal group law
A β-deformed version of motivic Segre classes of Schubert cells is constructed via the connective formal group law, with rational representatives via lattice models and structure constants via Knutson-Tao puzzles proven using quantum group intertwiners for d=1.
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Differential Forms and Hodge Structures on Singular Varieties
Introduces quasi-rational singularities and proves an isolated singularity is rational precisely when it is quasi-rational, Du Bois, and certain local mixed Hodge numbers vanish.
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Higher singularities for hypersurfaces
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
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Multigraded Regularity of the Complete Flag Variety
Proves inductive relationships and supplies inner and outer bounds on the multigraded regularity regions of the complete flag variety under the Plücker embedding.
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Noncommutative differential geometry of ambiskew polynomial rings
Sufficient criteria are given for ambiskew polynomial rings to be differentially smooth.