Journal of topology, ISSN 1753-8416, 2017, Volume 10, Issue 2, pp. 483 - 584

This paper is a sequel to ‘Shifted symplectic structures’ [T. Pantev, B. Toën, M. Vaquié and G. Vezzosi, Publ. Math. Inst. Hautes E'tudes Sci. 117 (2013)...

18G55 (primary) | 14A20 | 13D10 | MATHEMATICS | ALGEBRAS | Algebraic Geometry | Mathematics

18G55 (primary) | 14A20 | 13D10 | MATHEMATICS | ALGEBRAS | Algebraic Geometry | Mathematics

Journal Article

Selecta Mathematica, ISSN 1022-1824, 4/2017, Volume 23, Issue 2, pp. 1061 - 1119

We identify a class of quasi-compact semi-separated (qcss) twisted presheaves of algebras $$\mathcal {A}$$ A for which well-behaved Grothendieck abelian...

Mathematics, general | Mathematics | 13D10 | 14A22 | 18E15 | MATHEMATICS | FORMALITY | MATHEMATICS, APPLIED | COMPLEX | THEOREM | ALGEBRA | RINGS | HOCHSCHILD COHOMOLOGY | QUANTIZATION | CATEGORIES | SHEAVES | Algebra

Mathematics, general | Mathematics | 13D10 | 14A22 | 18E15 | MATHEMATICS | FORMALITY | MATHEMATICS, APPLIED | COMPLEX | THEOREM | ALGEBRA | RINGS | HOCHSCHILD COHOMOLOGY | QUANTIZATION | CATEGORIES | SHEAVES | Algebra

Journal Article

Letters in mathematical physics, ISSN 1573-0530, 2018, Volume 108, Issue 9, pp. 2055 - 2097

We describe some $$L_{\infty }$$ L∞ model for the local period map of a compact Kähler manifold. Applications include the study of deformations with associated...

Geometry | 32G20 | 14D07 | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | Yukawa algebra | L-infinity algebras | 13D10 | Physics | Formal period maps | LIE-ALGEBRAS | SPACE | COHOMOLOGY | DEFORMATIONS | CONSTRUCTION | MANIFOLDS | PHYSICS, MATHEMATICAL | HOMOTOPY-THEORY | GEOMETRY | Analysis | Algebra

Geometry | 32G20 | 14D07 | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | Yukawa algebra | L-infinity algebras | 13D10 | Physics | Formal period maps | LIE-ALGEBRAS | SPACE | COHOMOLOGY | DEFORMATIONS | CONSTRUCTION | MANIFOLDS | PHYSICS, MATHEMATICAL | HOMOTOPY-THEORY | GEOMETRY | Analysis | Algebra

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 12/2018, Volume 28, Issue 4, pp. 2984 - 3047

We introduce a natural map from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the infinitesimal...

Deformations | Secondary 13D10 | Deformations of complex structures | 53C55 | Primary 32G05 | Mathematics | 14D15 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Hermitian and Kählerian manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Deformations and infinitesimal methods | Formal methods | NUMBERS | Hermitian and Kahlerian manifolds | METRICS | EXTENSION | FORMULA | MATHEMATICS | COMPACT KAHLER MANIFOLD | CONE | GEOMETRY

Deformations | Secondary 13D10 | Deformations of complex structures | 53C55 | Primary 32G05 | Mathematics | 14D15 | Abstract Harmonic Analysis | Fourier Analysis | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Hermitian and Kählerian manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Deformations and infinitesimal methods | Formal methods | NUMBERS | Hermitian and Kahlerian manifolds | METRICS | EXTENSION | FORMULA | MATHEMATICS | COMPACT KAHLER MANIFOLD | CONE | GEOMETRY

Journal Article

INVENTIONES MATHEMATICAE, ISSN 0020-9910, 05/2020, Volume 220, Issue 2, pp. 581 - 610

We prove that the Hilbert scheme of points on a higher dimensional affine space is non-reduced and has components lying entirely in characteristic p for all...

SPACE | MATHEMATICS | 14B12 | 13D10 | MURPHYS-LAW | 14L30 | 14B07 | 14C05

SPACE | MATHEMATICS | 14B12 | 13D10 | MURPHYS-LAW | 14L30 | 14B07 | 14C05

Journal Article

Georgian mathematical journal, ISSN 1572-9176, 2018, Volume 25, Issue 4, pp. 529 - 544

Using homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a...

Kuranishi method | Deformation theory | 58K60 | formal deformation | 32S60 | 16S80 | 13D10 | 14B12 | 32G05 | 14B07 | 14D15 | deformation controlled by a differential graded Lie algebra | miniversal deformation | 32G08 | COMPLEX | YANG-MILLS CONNECTIONS | BUNDLES | SINGULARITIES | COALGEBRAS | LIE-ALGEBRAS | MATHEMATICS | SURFACE | GEOMETRY

Kuranishi method | Deformation theory | 58K60 | formal deformation | 32S60 | 16S80 | 13D10 | 14B12 | 32G05 | 14B07 | 14D15 | deformation controlled by a differential graded Lie algebra | miniversal deformation | 32G08 | COMPLEX | YANG-MILLS CONNECTIONS | BUNDLES | SINGULARITIES | COALGEBRAS | LIE-ALGEBRAS | MATHEMATICS | SURFACE | GEOMETRY

Journal Article

Forum Mathematicum, ISSN 0933-7741, 05/2015, Volume 27, Issue 3, pp. 1401 - 1434

In this paper, we study the moduli space of 4-dimensional complex associative algebras. We use extensions to compute the moduli space, and then give a...

16E40 | 17B55 | associative algebras | Versal deformations | 17B70 | 16S80 | 13D10 | 14B12 | 14D15 | MATHEMATICS | MATHEMATICS, APPLIED | RINGS | CLASSIFICATION | DEFORMATION

16E40 | 17B55 | associative algebras | Versal deformations | 17B70 | 16S80 | 13D10 | 14B12 | 14D15 | MATHEMATICS | MATHEMATICS, APPLIED | RINGS | CLASSIFICATION | DEFORMATION

Journal Article

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, ISSN 1815-0659, 2018, Volume 14, Issue 137

The complex Lie superalgebras g of type D(2, 1; a) - also denoted by osp (4, 2; a) - are usually considered for "non-singular" values of the parameter a, for...

singular degenerations | Lie superalgebras | PHYSICS, MATHEMATICAL | Lie supergroups | contractions | Order parameters | Mathematics | Representation Theory

singular degenerations | Lie superalgebras | PHYSICS, MATHEMATICAL | Lie supergroups | contractions | Order parameters | Mathematics | Representation Theory

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 10/2019, Volume 51, Issue 5, pp. 787 - 797

We study the degeneration relations on the varieties of associative and Lie algebra structures on a fixed finite‐dimensional vector space and give a...

13D10 (primary)

13D10 (primary)

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 5/2014, Volume 104, Issue 5, pp. 625 - 634

It is proven that, for any affine supermanifold M equipped with a constant odd symplectic structure, there is a universal action (up to homotopy) of the...

Geometry | Grothendieck–Teichmüller group | master equation | 81R99 | Theoretical, Mathematical and Computational Physics | Group Theory and Generalizations | 13D10 | Statistical Physics, Dynamical Systems and Complexity | Physics | Batalin–Vilkovisky algebras | Batalin-Vilkovisky algebras | Master equation | Grothendieck-Teichmüller group | Grothendieck-Teichmuller group | QUANTIZATION | PHYSICS, MATHEMATICAL

Geometry | Grothendieck–Teichmüller group | master equation | 81R99 | Theoretical, Mathematical and Computational Physics | Group Theory and Generalizations | 13D10 | Statistical Physics, Dynamical Systems and Complexity | Physics | Batalin–Vilkovisky algebras | Batalin-Vilkovisky algebras | Master equation | Grothendieck-Teichmüller group | Grothendieck-Teichmuller group | QUANTIZATION | PHYSICS, MATHEMATICAL

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 06/2018, Volume 50, Issue 3, pp. 449 - 461

We study divided power structures on finitely generated k‐algebras, where k is a field of positive characteristic p. As an application we show examples of...

13D10 (primary) | 13C40 | 14B07 (secondary) | MATHEMATICS

13D10 (primary) | 13C40 | 14B07 (secondary) | MATHEMATICS

Journal Article

Homology, Homotopy and Applications, ISSN 1532-0073, 2015, Volume 17, Issue 1, pp. 111 - 120

When studying deformations of an A-module M, Laudal and Yau showed that one can consider 1-cocycles in the Hochschild cohomology of A with coefficients in the...

Multi-module | Coefficient | Deformation | Hochschild | Higher order | Cohomology | Simplicial | MATHEMATICS | MATHEMATICS, APPLIED | cohomology | higher order | multi-module | coefficient | deformation | simplicial

Multi-module | Coefficient | Deformation | Hochschild | Higher order | Cohomology | Simplicial | MATHEMATICS | MATHEMATICS, APPLIED | cohomology | higher order | multi-module | coefficient | deformation | simplicial

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 12/2017, Volume 96, Issue 3, pp. 524 - 544

We investigate the relation between the Hodge theory of a smooth subcanonical n‐dimensional projective variety X and the deformation theory of the affine cone...

13D10 | 14B07 (primary) | 14C30 | 13D03 (secondary) | THREEFOLDS | MATHEMATICS | GRASSMANNIANS | MANIFOLDS | MIRROR SYMMETRY | Mathematics - Algebraic Geometry

13D10 | 14B07 (primary) | 14C30 | 13D03 (secondary) | THREEFOLDS | MATHEMATICS | GRASSMANNIANS | MANIFOLDS | MIRROR SYMMETRY | Mathematics - Algebraic Geometry

Journal Article

Manuscripta Mathematica, ISSN 0025-2611, 3/2014, Volume 143, Issue 3, pp. 419 - 443

The Hochschild cohomology of a DG algebra A with coefficients in itself is, up to a suspension of degrees, a graded Lie algebra. The purpose of this paper is...

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53D55 | 55P35 | 55P62 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 13D10 | MATHEMATICS | FREE LOOP SPACE | STRING TOPOLOGY | BAR | HOMOLOGY | CONSTRUCTION | Algebra

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 53D55 | 55P35 | 55P62 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 13D10 | MATHEMATICS | FREE LOOP SPACE | STRING TOPOLOGY | BAR | HOMOLOGY | CONSTRUCTION | Algebra

Journal Article

Communications in algebra, ISSN 0092-7872, 06/2020, pp. 1 - 11

Journal Article

Homology, Homotopy and Applications, ISSN 1532-0073, 2012, Volume 14, Issue 2, pp. 63 - 75

We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal....

Batalin-Vilkovisky algebra | Homotopical algebra | Differential graded Lie algebra | Deformation theory | Poisson manifold | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | homotopical algebra | differential graded Lie algebra | deformation theory | 13D10 | 18G55 | 53D17

Batalin-Vilkovisky algebra | Homotopical algebra | Differential graded Lie algebra | Deformation theory | Poisson manifold | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | homotopical algebra | differential graded Lie algebra | deformation theory | 13D10 | 18G55 | 53D17

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 08/2019, Volume 100, Issue 1, pp. 249 - 272

Consider the Hilbert scheme of points on a higher dimensional affine space. Its component is elementary if it parameterizes irreducible subschemes. We...

13D10 (secondary) | 14L30 | 14C05 (primary) | MATHEMATICS | ALGEBRAS | STRATA | FAMILIES | MURPHYS-LAW

13D10 (secondary) | 14L30 | 14C05 (primary) | MATHEMATICS | ALGEBRAS | STRATA | FAMILIES | MURPHYS-LAW

Journal Article

Collectanea Mathematica, ISSN 0010-0757, 9/2014, Volume 65, Issue 3, pp. 417 - 433

In this article we show that a wide range of multiple structures on curves arise whenever a family of embeddings degenerates to a morphism $$\varphi $$ φ of...

Multiple structures | 14J29 | Double structures | Mathematics | 13D10 | 14H45 | 14H10 | Geometry | Degenerations of curves | Algebra | 14B10 | Analysis | Applications of Mathematics | Deformation of morphisms | Locally non Cohen–Macaulay schemes | Locally non Cohen-Macaulay schemes | MATHEMATICS | MATHEMATICS, APPLIED | PROJECTIVE-SPACE | ROPES

Multiple structures | 14J29 | Double structures | Mathematics | 13D10 | 14H45 | 14H10 | Geometry | Degenerations of curves | Algebra | 14B10 | Analysis | Applications of Mathematics | Deformation of morphisms | Locally non Cohen–Macaulay schemes | Locally non Cohen-Macaulay schemes | MATHEMATICS | MATHEMATICS, APPLIED | PROJECTIVE-SPACE | ROPES

Journal Article

Revista Matemática Complutense, ISSN 1139-1138, 1/2013, Volume 26, Issue 1, pp. 253 - 269

In this article we give a condition, which holds in a very general setting, to smooth a rope, of any dimension, embedded in projective space. As a consequence...

14J29 | Canonical surface | Embedding | 14A15 | Mathematics | Topology | 13D10 | 14D06 | 14J10 | 14D15 | Geometry | Algebra | Rope | Smoothing | 14B10 | Analysis | Mathematics, general | Applications of Mathematics | Deformation of morphisms | MATHEMATICS | MATHEMATICS, APPLIED | MORPHISMS | GENERAL TYPE | DEFORMATION | SURFACES

14J29 | Canonical surface | Embedding | 14A15 | Mathematics | Topology | 13D10 | 14D06 | 14J10 | 14D15 | Geometry | Algebra | Rope | Smoothing | 14B10 | Analysis | Mathematics, general | Applications of Mathematics | Deformation of morphisms | MATHEMATICS | MATHEMATICS, APPLIED | MORPHISMS | GENERAL TYPE | DEFORMATION | SURFACES

Journal Article

Compositio mathematica, ISSN 0010-437X, 12/2017, Volume 153, Issue 12, pp. 2643 - 2657

In another direction: via the Riemann–Kempf singularity theorem [Kem73], one sees that the rulings on \(R_{L}\) cut out the linear series \(|L|\) and...

Bundling | Lower bounds | Cones | Loci | 14M12 | 13D10 (primary) | 14H51 | 14H60 | 14B10 | 14C34 (secondary)

Bundling | Lower bounds | Cones | Loci | 14M12 | 13D10 (primary) | 14H51 | 14H60 | 14B10 | 14C34 (secondary)

Journal Article

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