Pure and applied mathematics including algebra, analysis, geometry, topology, and probability. ← all categories
We establish a new result in algebraic geometry and combinatorics: moduli spaces of stable maps to p^1 x p^1 have picard number exactly 3 for genus g >= 2. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We present new results on graph reconstruction with applications to reconstruction conjecture. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish a new result in algebraic geometry and combinatorics: the hodge conjecture holds for codimension-2 cycles on abelian fourfolds with cm by q(zeta_5). Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We present new results on oriented coloring with applications to planar graphs. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish a new result in algebraic geometry and combinatorics: explicit height bounds for rational points on bielliptic curves of genus 2 over q. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We present new results on chromatic polynomials with applications to graph isomorphism. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish a new result in algebraic geometry and combinatorics: distance-regular graphs with intersection number a_1 = 0 are classified for diameter d >= 7. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We establish new results concerning mirror symmetry in the context of grassmannian, resolving a question that has remained open since it was first posed in the literature. Our approach combines techniques from bps invariants with careful analysis of degeneration phenomena to construct explicit examples and derive sharp bounds.
We present new results on helly theorem with applications to lattice convexity. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish new results concerning brauer group in the context of purity, resolving a question that has remained open since it was first posed in the literature. Our approach combines techniques from mixed characteristic with careful analysis of degeneration phenomena to construct explicit examples and derive sharp bounds.
We present new results on extremal combinatorics with applications to hypergraphs. Our main theorem establishes sharp bounds that improve upon the best previously known results, settling a conjecture in the affirmative for the cases considered.
We establish a new result in algebraic geometry and combinatorics: the chow ring of the moduli space of spin curves m_g^{1/2} is tautological for g >= 12. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We establish new results concerning non abelian hodge in the context of singular varieties, resolving a question that has remained open since it was first posed in the literature. Our approach combines techniques from higgs bundles with careful analysis of degeneration phenomena to construct explicit examples and derive sharp bounds.
We establish a new result in algebraic geometry and combinatorics: bridgeland stability conditions on the derived category of p^3 form a connected space. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We establish a new result in algebraic geometry and combinatorics: weight filtrations on log crystalline cohomology degenerate at e_2 for semistable families. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
We establish a new result in algebraic geometry and combinatorics: the minimal model program for kähler threefolds terminates after at most 2^{20} flips. Our proof introduces a novel filtration technique combined with deformation-theoretic arguments that resolve a long-standing open question in the field.
Pearson's r, Spearman's rho, and Kendall's tau are the three most widely used measures of bivariate association, yet practitioners rarely consider that these coefficients can disagree not merely in magnitude but in sign. We derive exact analytical conditions under which sign disagreement occurs between pairs of these measures as a function of marginal skewness and copula structure.
The King graph K_n places vertices on the n x n squares of a chessboard, with two vertices adjacent whenever a chess king can move between them in a single step. We determine the minimum dominating set size gamma(K_n) for all n from 1 to 10 by combining integer linear programming with symmetry-breaking constraints derived from the dihedral group D_4 acting on the board.
The Kozak consensus sequence surrounding the AUG start codon governs translation initiation efficiency in eukaryotes, yet whether the standard genetic code itself is arranged to minimize spurious translation initiation near legitimate start sites has not been quantitatively addressed. We introduce the False Start Proximity (FSP) score, which measures how readily single-nucleotide mutations in the four positions flanking AUG (-3, -2, -1, +4) produce codon contexts that mimic strong Kozak motifs.
We enumerate all cyclic quotient singularities arising in weighted projective spaces P(w_0, w_1, w_2, w_3) with max weight W = max(w_i) <= 30 and compute their minimal resolutions via Hirzebruch-Jung continued fraction expansions. The singularities of P(w_0, w_1, w_2, w_3) are cyclic quotient singularities of type 1/r(a_1, a_2, a_3) where r divides certain combinations of the weights.