Proceedings of the London Mathematical Society, ISSN 0024-6115, 03/2020, Volume 120, Issue 3, pp. 328 - 369

For each universal genus‐g polarization μ of degree d, we construct a universal tropical Jacobian Jμ,gtrop as a generalized cone complex over the moduli space...

14H40 | 14T05 (primary) | 14H10 | STACK | MATHEMATICS | MODULI SPACE | CURVES | COMPACTIFICATION | GEOMETRY

14H40 | 14T05 (primary) | 14H10 | STACK | MATHEMATICS | MODULI SPACE | CURVES | COMPACTIFICATION | GEOMETRY

Journal Article

Advances in geometry, ISSN 1615-7168, 2019, Volume 19, Issue 4, pp. 505 - 526

Let 𝓜 be the moduli space of compact connected hyperbolic surfaces of genus ≥ 2, and 𝓑 ⊂ 𝓜 its branch locus. Let be the Deligne–Mumford compactification of...

Primary 32G15 | stratification | noded Riemann surfaces | Moduli space | Secondary 14H10 | Loci | Strata

Primary 32G15 | stratification | noded Riemann surfaces | Moduli space | Secondary 14H10 | Loci | Strata

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 10/2005, Volume 130, Issue 1, pp. 1 - 37

We prove a localization formula for the moduli space of stable relative maps. As an application, we prove that all codimension i tautological classes on the...

MARINO-VAFA | MATHEMATICS | HODGE INTEGRALS | CHOW RINGS | HURWITZ NUMBERS | GROMOV-WITTEN-INVARIANTS | GENUS | PROOF | FORMULA | INTERSECTION THEORY | CONJECTURE | 14F43 | 14D22 | 14H10 | 14C15

MARINO-VAFA | MATHEMATICS | HODGE INTEGRALS | CHOW RINGS | HURWITZ NUMBERS | GROMOV-WITTEN-INVARIANTS | GENUS | PROOF | FORMULA | INTERSECTION THEORY | CONJECTURE | 14F43 | 14D22 | 14H10 | 14C15

Journal Article

Advances in Geometry, ISSN 1615-715X, 04/2018, Volume 18, Issue 2, pp. 161 - 180

We give a precise classification of the pairs ( , ) with a smooth curve of genus and ⊂ a curve of degree two and positive self-intersection. We prove that...

14H37 | Primary 14H45 | curve | curves in surfaces | Symmetric product | irregular surface | Secondary 14J25 | 14H10 | MATHEMATICS

14H37 | Primary 14H45 | curve | curves in surfaces | Symmetric product | irregular surface | Secondary 14J25 | 14H10 | MATHEMATICS

Journal Article

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

... singularities. Keywords Universal compacti ed Jacobians · Néron models Mathematics Subject Classi cation Primary 14H10; Secondary 14H40 1 Introduction Let f : X → B...

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

Experimental Mathematics, ISSN 1058-6458, 03/2011, Volume 20, Issue 1, pp. 34 - 56

We give a method for verifying, by a symbolic calculation, the stability or semistability with respect to a linearization of fixed, possibly small, degree m,...

Primary 14L24 | state polytope | 14H10; Secondary 14D22 | Hilbert stability | State polytope | MATHEMATICS | MODULI SPACE | GEOMETRIC INVARIANT-THEORY | CURVES | 14L24 | 14D22 | 13P10 | 14H10

Primary 14L24 | state polytope | 14H10; Secondary 14D22 | Hilbert stability | State polytope | MATHEMATICS | MODULI SPACE | GEOMETRIC INVARIANT-THEORY | CURVES | 14L24 | 14D22 | 13P10 | 14H10

Journal Article

Manuscripta Mathematica, ISSN 0025-2611, 5/2014, Volume 144, Issue 1, pp. 241 - 252

We determine the cohomology of the Losev–Manin moduli space $${\overline{M}_{0, 2 | n}}$$ M ¯ 0 , 2 | n of pointed genus zero curves as a representation of the...

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Secondary 14M25 | Mathematics, general | Algebraic Geometry | Mathematics | Primary 14H10 | Number Theory | TORIC VARIETIES | MATHEMATICS | CURVES

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Secondary 14M25 | Mathematics, general | Algebraic Geometry | Mathematics | Primary 14H10 | Number Theory | TORIC VARIETIES | MATHEMATICS | CURVES

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 08/2004, Volume 124, Issue 2, pp. 213 - 257

We construct a compactification M-d of the moduli space of lane curves of degree d. We regard-a plane curve C subset of P-2 as a surface-divisor pair (P-2, C),...

MATHEMATICS | SINGULARITIES | DEFORMATIONS | Mathematics - Algebraic Geometry | 14E30 | 14J10 | 14H10

MATHEMATICS | SINGULARITIES | DEFORMATIONS | Mathematics - Algebraic Geometry | 14E30 | 14J10 | 14H10

Journal Article

Collectanea mathematica (Barcelona), ISSN 2038-4815, 2018, Volume 70, Issue 1, pp. 107 - 115

... map · Wahl map Mathematics Subject Classiﬁcation Primary 14J28, 14H10 · Secondary 14H51 1 Introduction Let C be a complex projective nonsingular curve of genus...

Geometry | K3 surface | Secondary 14H51 | Algebra | Gaussian map | Primary 14J28 | Nodal curve | Analysis | Wahl map | Mathematics | Applications of Mathematics | 14H10 | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR SERIES

Geometry | K3 surface | Secondary 14H51 | Algebra | Gaussian map | Primary 14J28 | Nodal curve | Analysis | Wahl map | Mathematics | Applications of Mathematics | 14H10 | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR SERIES

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 10/2015, Volume 105, Issue 10, pp. 1427 - 1448

In a recent paper, Pandharipande, Solomon and Tessler initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. The...

Geometry | Riemann surfaces with boundary | moduli space | KdV equations | Theoretical, Mathematical and Computational Physics | Primary 35Q53 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | Physics | Secondary 14H10 | PHYSICS, MATHEMATICAL

Geometry | Riemann surfaces with boundary | moduli space | KdV equations | Theoretical, Mathematical and Computational Physics | Primary 35Q53 | Group Theory and Generalizations | Statistical Physics, Dynamical Systems and Complexity | Physics | Secondary 14H10 | PHYSICS, MATHEMATICAL

Journal Article

11.
Full Text
Equivariant cohomology of moduli spaces of genus three curves with level two structure

Geometriae dedicata, ISSN 1572-9168, 2018, Volume 202, Issue 1, pp. 165 - 191

We study the cohomology of the moduli space of genus three curves with level two structure and some related spaces. In particular, we determine the cohomology...

14N20 | Mathematics | Primary 14H10 | Topology | 14H50 | Plane quartics | Secondary 14F25 | 14J10 | Moduli spaces | Convex and Discrete Geometry | Equivariant cohomology | Algebraic Geometry | Hyperbolic Geometry | Del Pezzo surfaces | Projective Geometry | Differential Geometry | Curves of low genus | Configurations of point sets | MATHEMATICS | ABELIAN DIFFERENTIALS | Mathematics - Algebraic Geometry

14N20 | Mathematics | Primary 14H10 | Topology | 14H50 | Plane quartics | Secondary 14F25 | 14J10 | Moduli spaces | Convex and Discrete Geometry | Equivariant cohomology | Algebraic Geometry | Hyperbolic Geometry | Del Pezzo surfaces | Projective Geometry | Differential Geometry | Curves of low genus | Configurations of point sets | MATHEMATICS | ABELIAN DIFFERENTIALS | Mathematics - Algebraic Geometry

Journal Article

12.
Full Text
A chord diagrammatic presentation of the mapping class group of a once bordered surface

Geometriae Dedicata, ISSN 0046-5755, 2/2010, Volume 144, Issue 1, pp. 171 - 190

The Ptolemy groupoid is a combinatorial groupoid generated by elementary moves on marked trivalent fatgraphs with three types of relations. Through the...

Ribbon graphs | Ptolemy groupoid | Chord diagrams | Mathematics | 32G15 | Mapping class groups | Fatgraphs | 57M99 | 14H10 | Geometry | 20F38 | 05C25 | 20F34 | 20F99 | SPACE | MATHEMATICS | JOHNSON HOMOMORPHISMS | Business presentations

Ribbon graphs | Ptolemy groupoid | Chord diagrams | Mathematics | 32G15 | Mapping class groups | Fatgraphs | 57M99 | 14H10 | Geometry | 20F38 | 05C25 | 20F34 | 20F99 | SPACE | MATHEMATICS | JOHNSON HOMOMORPHISMS | Business presentations

Journal Article

Advances in Geometry, ISSN 1615-715X, 10/2018, Volume 18, Issue 4, pp. 451 - 465

We exploit an elementary specialization technique to study rational curves on Fano varieties of index one less than their dimension, known as del Pezzo...

Del Pezzo surface | Lefschetz pencil | 14N25 | 14N35 | Rational curve | Secondary 14N10 | Primary 14H10 | Fano variety of index | 14D05 | 1 | Gromov–Witten invariant | enumerative identity | normal bundle | Fano variety | Gromov-Witten invariant | Fano variety of index n-1 | ENUMERATIVE GEOMETRY | MATHEMATICS | NORMAL-BUNDLES | SPACE-CURVES

Del Pezzo surface | Lefschetz pencil | 14N25 | 14N35 | Rational curve | Secondary 14N10 | Primary 14H10 | Fano variety of index | 14D05 | 1 | Gromov–Witten invariant | enumerative identity | normal bundle | Fano variety | Gromov-Witten invariant | Fano variety of index n-1 | ENUMERATIVE GEOMETRY | MATHEMATICS | NORMAL-BUNDLES | SPACE-CURVES

Journal Article

Manuscripta Mathematica, ISSN 0025-2611, 5/2016, Volume 150, Issue 1, pp. 137 - 150

We determine the action of the product of symmetric groups on the cohomology of certain moduli of weighted pointed rational curves. The moduli spaces that we...

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Secondary 20C30 | Mathematics, general | Algebraic Geometry | Mathematics | Primary 14H10 | 14D22 | Number Theory | OPERADS | MATHEMATICS | SPACES | Mathematics - Algebraic Geometry

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Secondary 20C30 | Mathematics, general | Algebraic Geometry | Mathematics | Primary 14H10 | 14D22 | Number Theory | OPERADS | MATHEMATICS | SPACES | Mathematics - Algebraic Geometry

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 12/2019, Volume 119, Issue 6, pp. 1431 - 1463

We give an inductive proof that the generalized Severi varieties — the varieties which parametrize (irreducible) plane curves of given degree and genus, with a...

14D06 (primary) | 14H50 | 14H10

14D06 (primary) | 14H50 | 14H10

Journal Article

Collectanea Mathematica, ISSN 0010-0757, 5/2015, Volume 66, Issue 2, pp. 191 - 202

Harris and Morrison (Invent. Math. 99:321–355, 1990, Theorem 2.5), constructed certain semistable fibrations $$f:F\rightarrow Y$$ f : F → Y in $$k$$ k -gonal...

Geometry | Algebra | Analysis | Fibration | Gonality | Mathematics | 14H51 | Applications of Mathematics | Moduli of curves | Primary 14D22 | Secondary 14H10 | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAIC-SURFACES | MODULI SPACE | GENERAL TYPE | INDEX | CURVES | GEOGRAPHY

Geometry | Algebra | Analysis | Fibration | Gonality | Mathematics | 14H51 | Applications of Mathematics | Moduli of curves | Primary 14D22 | Secondary 14H10 | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAIC-SURFACES | MODULI SPACE | GENERAL TYPE | INDEX | CURVES | GEOGRAPHY

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 02/2018, Volume 50, Issue 1, pp. 148 - 158

Let X be a del Pezzo surface of degree 5 defined over a field F. A theorem of Manin and Swinnerton‐Dyer asserts that every Del Pezzo surface of degree 5 is...

14E08 | 20G15 | 14M20 (primary) | 16K50 | 14H10

14E08 | 20G15 | 14M20 (primary) | 16K50 | 14H10

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 09/2019, Volume 119, Issue 3, pp. 781 - 813

We study the orbifold Gromov–Witten theory of the quotient [C3/Z3] in all genera. Our first result is a proof of the holomorphic anomaly equations in the...

14N35 | 53D45 (primary) | 14H10 | MATHEMATICS | COHOMOLOGY | LEFSCHETZ | QUANTUM RIEMANN-ROCH

14N35 | 53D45 (primary) | 14H10 | MATHEMATICS | COHOMOLOGY | LEFSCHETZ | QUANTUM RIEMANN-ROCH

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 8/2012, Volume 271, Issue 3, pp. 953 - 960

We prove the irreducibility of universal Severi varieties parametrizing irreducible, reduced, nodal hyperplane sections of primitive K3 surfaces of genus g,...

Mathematics, general | Mathematics | GAUSSIAN MAPS | MATHEMATICS | NODAL CURVES | K-3 SURFACES | RATIONAL CURVES | CANONICAL CURVES | Algebraic Geometry

Mathematics, general | Mathematics | GAUSSIAN MAPS | MATHEMATICS | NODAL CURVES | K-3 SURFACES | RATIONAL CURVES | CANONICAL CURVES | Algebraic Geometry

Journal Article

Selecta Mathematica, ISSN 1022-1824, 1/2016, Volume 22, Issue 1, pp. 417 - 445

In this paper, we study the topology of the stack $$\mathcal {T}_g$$ T g of smooth trigonal curves of genus g over the complex field. We make use of a...

Secondary 14H30 | Trigonal curves | 14D23 | Mathematics | Monodromy maps | Primary 14H10 | 32G15 | Mapping class groups | Hurwitz spaces | Moduli stacks of curves | Braid groups | Teichmüller spaces | Mathematics, general | Orbifold fundamental group | MATHEMATICS, APPLIED | MONODROMY GROUPS | Teichmuller spaces | SINGULARITIES | CYCLIC COVERS | SYMMETRIC VANISHING LATTICES | 3-FOLD BRANCHED-COVERINGS | CHOW RING | STACKS | CURVES | MATHEMATICS | FUNDAMENTAL-GROUPS | SURFACES | Algebraic Geometry

Secondary 14H30 | Trigonal curves | 14D23 | Mathematics | Monodromy maps | Primary 14H10 | 32G15 | Mapping class groups | Hurwitz spaces | Moduli stacks of curves | Braid groups | Teichmüller spaces | Mathematics, general | Orbifold fundamental group | MATHEMATICS, APPLIED | MONODROMY GROUPS | Teichmuller spaces | SINGULARITIES | CYCLIC COVERS | SYMMETRIC VANISHING LATTICES | 3-FOLD BRANCHED-COVERINGS | CHOW RING | STACKS | CURVES | MATHEMATICS | FUNDAMENTAL-GROUPS | SURFACES | Algebraic Geometry

Journal Article

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