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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
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
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
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 12/2018, Volume 28, Issue 4, pp. 2984 - 3047
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
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
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
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
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)
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 5/2014, Volume 104, Issue 5, pp. 625 - 634
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
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
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
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
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
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
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
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
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)
Journal Article
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