Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 346, pp. 1091 - 1136

We show that the combinatorial structure of the compactified universal Jacobians over M‾g in degrees g...

Moduli of stable curves | Graph | Compactified Jacobian | Orientation | SPACE | MATHEMATICS | TORELLI THEOREM | TROPICALIZATION | MODULI | GEOMETRY

Moduli of stable curves | Graph | Compactified Jacobian | Orientation | SPACE | MATHEMATICS | TORELLI THEOREM | TROPICALIZATION | MODULI | GEOMETRY

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2017, Volume 369, Issue 8, pp. 5341 - 5402

To every singular reduced projective curve X one can associate many fine compactified Jacobians, depending on the choice of a polarization on X, each of which yields a modular compactification...

Locally planar singularities | Abel map | Compactified jacobians | MATHEMATICS | SCHEME | AUTODUALITY | BUNDLES | locally planar singularities | Compactified Jacobians | DUALITY | ABEL MAPS | FUNDAMENTAL LEMMA

Locally planar singularities | Abel map | Compactified jacobians | MATHEMATICS | SCHEME | AUTODUALITY | BUNDLES | locally planar singularities | Compactified Jacobians | DUALITY | ABEL MAPS | FUNDAMENTAL LEMMA

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 01/2013, Volume 120, Issue 1, pp. 49 - 63

J. Piontkowski described the homology of the Jacobi factor of a plane curve singularity with one Puiseux pair. We discuss the combinatorial structure of his...

Compactified Jacobians | [formula omitted]-Catalan numbers | Hilbert schemes | Q, t-Catalan numbers | MATHEMATICS | HILBERT SCHEME | STATISTICS | HOMOLOGY | CURVES | q, t-Catalan numbers

Compactified Jacobians | [formula omitted]-Catalan numbers | Hilbert schemes | Q, t-Catalan numbers | MATHEMATICS | HILBERT SCHEME | STATISTICS | HOMOLOGY | CURVES | q, t-Catalan numbers

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 06/2012, Volume 285, Issue 8‐9, pp. 997 - 1031

We study Esteves's fine compactified Jacobians for nodal curves. We give a proof of the fact that, for a...

Fine and coarse compactified Jacobians | 14H40 | 14D22 | nodal curves | Néron models | MSC 14H10 | Nodal curves | PICARD | MODULI | FUNDAMENTAL LEMMA | MATHEMATICS | STABLE CURVES | ABEL MAPS | Neron models | GEOMETRY | SCHEMES | Mathematics - Algebraic Geometry

Fine and coarse compactified Jacobians | 14H40 | 14D22 | nodal curves | Néron models | MSC 14H10 | Nodal curves | PICARD | MODULI | FUNDAMENTAL LEMMA | MATHEMATICS | STABLE CURVES | ABEL MAPS | Neron models | GEOMETRY | SCHEMES | Mathematics - Algebraic Geometry

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 10/2015, Volume 17, Issue 5, p. 1450046

Let Y → ℙn be a flat family of reduced Gorenstein curves, such that the compactified relative Jacobian $X = \overline{J}^d(Y/{\mathbb P}^n...

Holomorphic symplectic manifolds | Jacobians of curves | Lagrangian fibrations | MATHEMATICS | MATHEMATICS, APPLIED | COMPACTIFIED JACOBIANS | ABEL MAPS | CURVES | Mathematical analysis | Flats | Jacobians | Mathematics - Algebraic Geometry

Holomorphic symplectic manifolds | Jacobians of curves | Lagrangian fibrations | MATHEMATICS | MATHEMATICS, APPLIED | COMPACTIFIED JACOBIANS | ABEL MAPS | CURVES | Mathematical analysis | Flats | Jacobians | Mathematics - Algebraic Geometry

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 2/2014, Volume 39, Issue 1, pp. 153 - 186

... polynomials of compactified Jacobians of plane curve singularities x kn±1=y n . We also give a geometric interpretation of a relation between rational-slope Catalan numbers and the theory of (m,n...

Convex and Discrete Geometry | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Semigroup | q , t -Catalan numbers | Compactified Jacobian | Combinatorics | Computer Science, general | q,t-Catalan numbers | MATHEMATICS | STATISTICS | PARTITIONS | CURVES | q, t-Catalan numbers

Convex and Discrete Geometry | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Semigroup | q , t -Catalan numbers | Compactified Jacobian | Combinatorics | Computer Science, general | q,t-Catalan numbers | MATHEMATICS | STATISTICS | PARTITIONS | CURVES | q, t-Catalan numbers

Journal Article

Bollettino dell'Unione Matematica Italiana, ISSN 1972-6724, 9/2017, Volume 10, Issue 3, pp. 321 - 334

In the present paper we consider the following question: does there exist a Néron model for families of Jacobians of curves with sections...

Mathematics, general | Secondary 14H40 | Mathematics | Primary 14H10 | Universal compactified Jacobians | Néron models

Mathematics, general | Secondary 14H40 | Mathematics | Primary 14H10 | Universal compactified Jacobians | Néron models

Journal Article

Communications in Algebra, ISSN 0092-7872, 04/2019, Volume 47, Issue 4, pp. 1385 - 1389

In this article, we study the irreducible components of the compactified Jacobian of a ribbon X of arithmetic genus g over a smooth curve of genus...

Compactified Jacobians | ribbons | multiple curves | generalized line bundles | MATHEMATICS | BUNDLES | 14D20 | 14H60 | 14H40 | Mathematics - Algebraic Geometry

Compactified Jacobians | ribbons | multiple curves | generalized line bundles | MATHEMATICS | BUNDLES | 14D20 | 14H60 | 14H40 | Mathematics - Algebraic Geometry

Journal Article

Journal of Algebra, ISSN 0021-8693, 11/2012, Volume 370, pp. 326 - 343

This paper studies the components of the moduli space of rank 1, torsion-free sheaves, or compactified Jacobian, of a non-Gorenstein curve...

Rank 1 | Compactified Jacobian | Hilbert scheme | Torsion-free sheaf | Secondary | Primary | MATHEMATICS | CURVE SINGULARITIES | POINTS | SCHEMES

Rank 1 | Compactified Jacobian | Hilbert scheme | Torsion-free sheaf | Secondary | Primary | MATHEMATICS | CURVE SINGULARITIES | POINTS | SCHEMES

Journal Article

Algebra and Number Theory, ISSN 1937-0652, 2013, Volume 7, Issue 2, pp. 379 - 404

We provide sufficient conditions for the line bundle locus in a family of compact moduli spaces of pure sheaves to be isomorphic to the Neron model. The result...

Néron model | Compactified Jacobian | Relative Picard functor | Stable sheaf | MATHEMATICS | STABLE CURVES | FIELDS | Neron model | COMPACTIFIED JACOBIANS | stable sheaf | NERON MODELS | compactified Jacobian | PICARD SCHEME | MODULI | SHEAVES | relative Picard functor

Néron model | Compactified Jacobian | Relative Picard functor | Stable sheaf | MATHEMATICS | STABLE CURVES | FIELDS | Neron model | COMPACTIFIED JACOBIANS | stable sheaf | NERON MODELS | compactified Jacobian | PICARD SCHEME | MODULI | SHEAVES | relative Picard functor

Journal Article

Advances in Mathematics, ISSN 0001-8708, 12/2017, Volume 321, pp. 221 - 268

The Jacobian varieties of smooth curves fit together to form a family, the universal Jacobian, over the moduli space of smooth pointed curves, and the theta divisors of these curves form a divisor...

Wall-crossing | Moduli of curves | Compactified Jacobian | Universal Jacobian | Theta divisor | VARIETY | REDUCED CURVES | BUNDLES | MARKED POINTS | MODULI STACK | (M)OVER-BAR(G) | MATHEMATICS | STABLE CURVES | JACOBIANS | COMPACTIFIED PICARD STACKS | Mathematics - Algebraic Geometry

Wall-crossing | Moduli of curves | Compactified Jacobian | Universal Jacobian | Theta divisor | VARIETY | REDUCED CURVES | BUNDLES | MARKED POINTS | MODULI STACK | (M)OVER-BAR(G) | MATHEMATICS | STABLE CURVES | JACOBIANS | COMPACTIFIED PICARD STACKS | Mathematics - Algebraic Geometry

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2009, Volume 11, Issue 6, pp. 1385 - 1427

The object of this paper is the theta divisor of the compactified jacobian of a nodal curve...

Compactified picard scheme | Nodal curve | Abel map | Line bundle | Theta divisor | Hyperelliptic stable curve | MATHEMATICS | line bundle | hyperelliptic stable curve | MATHEMATICS, APPLIED | compactified Picard scheme | theta divisor | VARIETIES | AMPLENESS | CURVES | MODULI

Compactified picard scheme | Nodal curve | Abel map | Line bundle | Theta divisor | Hyperelliptic stable curve | MATHEMATICS | line bundle | hyperelliptic stable curve | MATHEMATICS, APPLIED | compactified Picard scheme | theta divisor | VARIETIES | AMPLENESS | CURVES | MODULI

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 09/2018, Volume 25, Issue 3

We apply lattice point techniques to the study of simultaneous core partitions. Our central observation is that for a and b relatively prime, the abacus...

MATHEMATICS | MATHEMATICS, APPLIED | ARMSTRONGS CONJECTURE | COMPACTIFIED JACOBIANS | CATALAN NUMBERS

MATHEMATICS | MATHEMATICS, APPLIED | ARMSTRONGS CONJECTURE | COMPACTIFIED JACOBIANS | CATALAN NUMBERS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2005, Volume 198, Issue 2, pp. 484 - 503

... ¯ , which maps C into its compactified Jacobian, and form its pullback map A L * : Pic J ¯ 0 → J , which carries the connected component of 0 in the Picard scheme back to the Jacobian...

Autoduality | Compactified Jacobian | Curves with double points | MATHEMATICS | compactified Jacobian | curves with double points | autoduality

Autoduality | Compactified Jacobian | Curves with double points | MATHEMATICS | compactified Jacobian | curves with double points | autoduality

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2016, Volume 368, Issue 12, pp. 8403 - 8445

We introduce a new approach to the enumeration of rational slope parking functions with respect to the \operatorname {area} and a generalized \operatorname...

Affine permutations | Parking functions | MATHEMATICS | COMPACTIFIED JACOBIANS | SYMMETRY | REPRESENTATIONS | NUMBERS | affine permutations | FIXED-POINT VARIETIES | SHI ARRANGEMENT | SPRINGER FIBERS | COMBINATORICS

Affine permutations | Parking functions | MATHEMATICS | COMPACTIFIED JACOBIANS | SYMMETRY | REPRESENTATIONS | NUMBERS | affine permutations | FIXED-POINT VARIETIES | SHI ARRANGEMENT | SPRINGER FIBERS | COMBINATORICS

Journal Article

Journal of Algebra, ISSN 0021-8693, 02/2019, Volume 520, pp. 186 - 236

...; explicit formulas are obtained for torus knots. The new feature is the definition of counterparts of Jacobian factors...

Algebraic knot | Hecke algebra | Khovanov–Rozansky homology | Macdonald polynomial | Compactified Jacobian | Puiseux expansion | Plane curve singularity | Orbital integral | HILBERT SCHEMES | COMPACTIFIED JACOBIANS | MATRIX FACTORIZATIONS | KNOTS | T-CATALAN NUMBERS | MATHEMATICS | SUPPORT | Khovanov-Rozansky homology | LINK HOMOLOGY | HALL ALGEBRA | Algebra

Algebraic knot | Hecke algebra | Khovanov–Rozansky homology | Macdonald polynomial | Compactified Jacobian | Puiseux expansion | Plane curve singularity | Orbital integral | HILBERT SCHEMES | COMPACTIFIED JACOBIANS | MATRIX FACTORIZATIONS | KNOTS | T-CATALAN NUMBERS | MATHEMATICS | SUPPORT | Khovanov-Rozansky homology | LINK HOMOLOGY | HALL ALGEBRA | Algebra

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2014, Volume 263, pp. 88 - 122

We calculate the Borel–Moore homology of affine Springer fibers of type A associated with some regular semisimple nil elliptic elements. As a result, we obtain...

Affine Springer fibers | Diagonal coinvariants | MATHEMATICS | COMPACTIFIED JACOBIANS | CHARACTER | FIXED-POINT VARIETIES | CONJUGACY CLASSES | Fibers

Affine Springer fibers | Diagonal coinvariants | MATHEMATICS | COMPACTIFIED JACOBIANS | CHARACTER | FIXED-POINT VARIETIES | CONJUGACY CLASSES | Fibers

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 09/2015, Volume 104, Issue 3, pp. 403 - 435

We consider the construction of refined Chern–Simons torus knot invariants by M. Aganagic and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a...

Torus knots | Hilbert scheme | Double affine Hecke algebra | 14F05 | 14C05 | 55A25 | TESLER MATRICES | ELLIPTIC HALL ALGEBRA | MATHEMATICS, APPLIED | COMPACTIFIED JACOBIANS | HECKE ALGEBRAS | AFFINE SPRINGER FIBERS | FINITE-DIMENSIONAL REPRESENTATIONS | RATIONAL CHEREDNIK ALGEBRAS | T-CATALAN NUMBERS | MATHEMATICS | FIXED-POINT VARIETIES | QUOTIENT RING | Algebra

Torus knots | Hilbert scheme | Double affine Hecke algebra | 14F05 | 14C05 | 55A25 | TESLER MATRICES | ELLIPTIC HALL ALGEBRA | MATHEMATICS, APPLIED | COMPACTIFIED JACOBIANS | HECKE ALGEBRAS | AFFINE SPRINGER FIBERS | FINITE-DIMENSIONAL REPRESENTATIONS | RATIONAL CHEREDNIK ALGEBRAS | T-CATALAN NUMBERS | MATHEMATICS | FIXED-POINT VARIETIES | QUOTIENT RING | Algebra

Journal Article

Research in the Mathematical Sciences, ISSN 2522-0144, 12/2017, Volume 4, Issue 1, pp. 1 - 11

We prove that certain degenerate abelian varieties that include compactified Jacobians, namely stable semiabelic varieties, satisfy autoduality...

Computational Mathematics and Numerical Analysis | 14D20 | Autoduality | Mathematics, general | Compactified Jacobians | Mathematics | Applications of Mathematics | Stable abelic variety | Secondary 14K30 | Primary 14H40 | MATHEMATICS | MAPS | SINGULARITIES | CURVES | MODULI

Computational Mathematics and Numerical Analysis | 14D20 | Autoduality | Mathematics, general | Compactified Jacobians | Mathematics | Applications of Mathematics | Stable abelic variety | Secondary 14K30 | Primary 14H40 | MATHEMATICS | MAPS | SINGULARITIES | CURVES | MODULI

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 01/2017, Volume 145, pp. 57 - 100

Our main result here is that the specialization at t=1/q of the Qkm,kn operators studied in Bergeron et al. [2] may be given a very simple plethystic form....

Plethysm | Shuffle conjecture | Parking function | POLYNOMIALS | MATHEMATICS | ELLIPTIC HALL ALGEBRA | COMPACTIFIED JACOBIANS | NUMBERS

Plethysm | Shuffle conjecture | Parking function | POLYNOMIALS | MATHEMATICS | ELLIPTIC HALL ALGEBRA | COMPACTIFIED JACOBIANS | NUMBERS

Journal Article

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