Inventiones mathematicae, ISSN 0020-9910, 10/2019, Volume 218, Issue 1, pp. 197 - 299

Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special...

Mathematics, general | Mathematics | 14D20 | 14H60 | 14F45

Mathematics, general | Mathematics | 14D20 | 14H60 | 14F45

Journal Article

Osaka Journal of Mathematics, ISSN 0030-6126, 01/2014, Volume 51, Issue 1, pp. 203 - 213

Let X be a Calabi-Yau threefold and mu the symmetric trilinear form on the second cohomology group H-2(X, Z) defined by the cup product. We investigate the...

MATHEMATICS | EULER NUMBER | 14J32 | 14F45

MATHEMATICS | EULER NUMBER | 14J32 | 14F45

Journal Article

Mathematische Annalen, ISSN 0025-5831, 2/2019, Volume 373, Issue 1, pp. 397 - 419

We show that many spin 6-manifolds have the homotopy type but not the homeomorphism type of a Kähler manifold. Moreover, for given Betti numbers, there are...

32Q15 | 57R15 | Secondary 14E30 | Mathematics, general | Mathematics | Primary 14F45 | 57R20 | MATHEMATICS | BUNDLES

32Q15 | 57R15 | Secondary 14E30 | Mathematics, general | Mathematics | Primary 14F45 | 57R20 | MATHEMATICS | BUNDLES

Journal Article

Communications in Algebra, ISSN 0092-7872, 06/2019, Volume 47, Issue 6, pp. 2540 - 2547

During the conference held in 2017 in Minneapolis for his 60th birthday, Gennady Lyubeznik proposed the following problem: Find a complete local domain R and...

13G05 | Lyubeznik complex | domain | hyperplane sections | Connectedness | nerve complex | 14F45 | MATHEMATICS | MULTIPLICITY | GROBNER BASES | IDEALS | Domains | Hyperplanes

13G05 | Lyubeznik complex | domain | hyperplane sections | Connectedness | nerve complex | 14F45 | MATHEMATICS | MULTIPLICITY | GROBNER BASES | IDEALS | Domains | Hyperplanes

Journal Article

5.
Full Text
The monodromy theorem for compact Kähler manifolds and smooth quasi-projective varieties

Mathematische Annalen, ISSN 0025-5831, 8/2018, Volume 371, Issue 3, pp. 1069 - 1086

Given any connected topological space X, assume that there exists an epimorphism $$\phi {:}\; \pi _1(X) \rightarrow {\mathbb {Z}}$$ ϕ:π1(X)→Z . The deck...

Mathematics, general | Mathematics | 32S40 | 14F45 | COMPLEMENTS | MATHEMATICS | COHOMOLOGY JUMP LOCI

Mathematics, general | Mathematics | 32S40 | 14F45 | COMPLEMENTS | MATHEMATICS | COHOMOLOGY JUMP LOCI

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 2015, Volume 176, Issue 1, pp. 241 - 269

Given a smooth toric variety X, the action of the torus T lifts to the moduli space M of stable sheaves on X. Using the pioneering work of Klyacho, a fairly...

Moduli spaces of sheaves | Toric surfaces | Configurations of linear subspaces | Generating functions | Geometry | 14N20 | 14M25 | Mathematics | 14J60 | 14F45 | MATHEMATICS | HILBERT SCHEME | BUNDLES | BETTI NUMBERS | INVARIANTS | VARIETIES | STACKS | POINTS | Mathematics - Algebraic Geometry

Moduli spaces of sheaves | Toric surfaces | Configurations of linear subspaces | Generating functions | Geometry | 14N20 | 14M25 | Mathematics | 14J60 | 14F45 | MATHEMATICS | HILBERT SCHEME | BUNDLES | BETTI NUMBERS | INVARIANTS | VARIETIES | STACKS | POINTS | Mathematics - Algebraic Geometry

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 06/2015, Volume 219, Issue 6, pp. 2279 - 2299

Let K be a finite simplicial complex, and (X,A) be a pair of spaces. The purpose of this article is to study the fundamental group of the polyhedral product...

ARTIN GROUPS | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Algebraic Topology

ARTIN GROUPS | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Algebraic Topology

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 2012, Volume 161, Issue 7, pp. 1351 - 1378

Suppose that g >= 3, that n >= 0, and that l >= 1. The main result is that if E is a smooth variety that dominates a codimension 1 subvariety D of M-g,M-n [l],...

MATHEMATICS | MODULI SPACE | 14H15 | 14D05 | 14F35 | 14F45

MATHEMATICS | MODULI SPACE | 14H15 | 14D05 | 14F35 | 14F45

Journal Article

Results in Mathematics, ISSN 1422-6383, 9/2019, Volume 74, Issue 3, pp. 1 - 22

Let X be a complex, irreducible, quasi-projective variety, and $$\pi :{\widetilde{X}}\rightarrow X$$ π:X~→X a resolution of singularities of X. Assume that the...

14F05 | 14M15 | Poincaré polynomial | 32S60 | Schubert varieties | 14F43 | 58K15 | Mathematics | Primary 14B05 | smooth fibration | derived category | Secondary 14E15 | Projective variety | 14F45 | Betti numbers | 32S20 | resolution of singularities | Mathematics, general | intersection cohomology | Decomposition Theorem | TOPOLOGY | MATHEMATICS, APPLIED | MATHEMATICS | Poincare polynomial | SHEAVES

14F05 | 14M15 | Poincaré polynomial | 32S60 | Schubert varieties | 14F43 | 58K15 | Mathematics | Primary 14B05 | smooth fibration | derived category | Secondary 14E15 | Projective variety | 14F45 | Betti numbers | 32S20 | resolution of singularities | Mathematics, general | intersection cohomology | Decomposition Theorem | TOPOLOGY | MATHEMATICS, APPLIED | MATHEMATICS | Poincare polynomial | SHEAVES

Journal Article

Revista Matemática Complutense, ISSN 1139-1138, 5/2019, Volume 32, Issue 2, pp. 419 - 450

This paper deals with the invariant $$R_X$$ R X called the RR-correction term, which appears in the Riemann–Roch and Numerical Adjunction Formulas for normal...

Adjunction formula | Curvettes | Mathematics | McKay correspondence | Topology | Riemann-Roch | 14H50 | Cyclic quotient singularities | 14F45 | Geometry | 32S25 | Algebra | Reflexive modules | Analysis | Mathematics, general | Applications of Mathematics | 32S05 | MATHEMATICS | MATHEMATICS, APPLIED

Adjunction formula | Curvettes | Mathematics | McKay correspondence | Topology | Riemann-Roch | 14H50 | Cyclic quotient singularities | 14F45 | Geometry | 32S25 | Algebra | Reflexive modules | Analysis | Mathematics, general | Applications of Mathematics | 32S05 | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 10/2017, Volume 190, Issue 1, pp. 1 - 22

For a fixed compact Riemann surface X, of genus at least 2, we count the number of connected components of the moduli space of maximal Higgs bundles over X for...

Geometry | Moduli spaces | Higgs bundles | Connected components | Secondary 14D20 | 14C30 | Hermitian groups | Mathematics | Cayley correspondence | Primary 14H60 | 14F45 | MATHEMATICS | SURFACE GROUP-REPRESENTATIONS | Mathematics - Differential Geometry

Geometry | Moduli spaces | Higgs bundles | Connected components | Secondary 14D20 | 14C30 | Hermitian groups | Mathematics | Cayley correspondence | Primary 14H60 | 14F45 | MATHEMATICS | SURFACE GROUP-REPRESENTATIONS | Mathematics - Differential Geometry

Journal Article

Experimental Mathematics, ISSN 1058-6458, 10/2017, Volume 26, Issue 4, pp. 490 - 495

We study a surface discovered by Stover which is the surface with minimal Euler number and maximal automorphism group among smooth arithmetic ball quotient...

ball quotient surfaces | Secondary 14J25, 14F45 | Primary 14F35, 14J29 | Hurwitz ball quotients | Lagrangian surfaces | MATHEMATICS | VARIETIES | Algebraic Geometry | Mathematics

ball quotient surfaces | Secondary 14J25, 14F45 | Primary 14F35, 14J29 | Hurwitz ball quotients | Lagrangian surfaces | MATHEMATICS | VARIETIES | Algebraic Geometry | Mathematics

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2015, Volume 43, Issue 8, pp. 3051 - 3072

Let X be a smooth projective complex curve. We prove that a Torelli type theorem holds, under certain conditions, for the moduli space of α-polystable...

Moduli spaces | Vector bundles | Quadratic pairs | Secondary: 14D20, 14C30, 14F45 | Primary: 14H60 | MATHEMATICS | REPRESENTATIONS | HITCHIN PAIRS | SURFACE | ALGEBRAIC CURVE | VECTOR-BUNDLES

Moduli spaces | Vector bundles | Quadratic pairs | Secondary: 14D20, 14C30, 14F45 | Primary: 14H60 | MATHEMATICS | REPRESENTATIONS | HITCHIN PAIRS | SURFACE | ALGEBRAIC CURVE | VECTOR-BUNDLES

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 4/2017, Volume 187, Issue 1, pp. 123 - 135

We prove Barth-type connectedness results for low-codimension smooth subvarieties with good numerical properties inside certain “easy” ambient spaces (such as...

Spherical varieties | 14M27 | 14M15 | Positivity | Cones of cycle classes | Mathematics | 14C99 | 14F45 | Geometry | Barth theorem | Connectedness | 14M07 | 14M17 | Homogeneous varieties | PROJECTIVE-SPACE | SUBVARIETIES | CONES | HOMOGENEOUS SPACES | CONIVEAU | PICARD GROUP | MATHEMATICS | SMALL CODIMENSION | Mathematics - Algebraic Geometry

Spherical varieties | 14M27 | 14M15 | Positivity | Cones of cycle classes | Mathematics | 14C99 | 14F45 | Geometry | Barth theorem | Connectedness | 14M07 | 14M17 | Homogeneous varieties | PROJECTIVE-SPACE | SUBVARIETIES | CONES | HOMOGENEOUS SPACES | CONIVEAU | PICARD GROUP | MATHEMATICS | SMALL CODIMENSION | Mathematics - Algebraic Geometry

Journal Article

Algebraic Geometry, ISSN 2214-2584, 01/2018, Volume 5, Issue 1, pp. 1 - 14

We provide families of affine threefolds which are $\mathbb A^1$-contractible (that is, contractible in the unstable $\mathbb A^1$-homotopy category of...

Algebraic Geometry | Mathematics

Algebraic Geometry | Mathematics

Journal Article

Communications in Algebra, ISSN 0092-7872, 06/2016, Volume 44, Issue 6, pp. 2547 - 2560

Let Y ⊆ ℙ N be a possibly singular projective variety, defined over the field of complex numbers. Let X be the intersection of Y with h general hypersurfaces...

Singularity | 14F17 | 14M10 | Chow variety | Algebraic cycle | 14J17 | 14C25 | 14F43 | Projective variety | 14C05 | 14C15 | 14F45 | Algebraic equivalence | Connectivity Theorem | Hilbert scheme | Homological equivalence | Integers | Complex numbers | Geometry | Algebra | Equivalence | Constrictions | Homology | Intersections

Singularity | 14F17 | 14M10 | Chow variety | Algebraic cycle | 14J17 | 14C25 | 14F43 | Projective variety | 14C05 | 14C15 | 14F45 | Algebraic equivalence | Connectivity Theorem | Hilbert scheme | Homological equivalence | Integers | Complex numbers | Geometry | Algebra | Equivalence | Constrictions | Homology | Intersections

Journal Article

Geometry and Topology, ISSN 1465-3060, 02/2015, Volume 19, Issue 1, pp. 295 - 342

For any symmetric collection (h(p,q))(p+q=k) of natural numbers, we construct a smooth complex projective variety X whose weight-k Hodge structure has Hodge...

KAHLER-MANIFOLDS | MATHEMATICS | CALABI-YAU | GEOMETRY

KAHLER-MANIFOLDS | MATHEMATICS | CALABI-YAU | GEOMETRY

Journal Article

Jahresbericht der Deutschen Mathematiker-Vereinigung, ISSN 0012-0456, 9/2016, Volume 118, Issue 3, pp. 143 - 178

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 4/2017, Volume 111, Issue 2, pp. 377 - 402

In a previous work, the third named author found a combinatorics of line arrangements whose realizations live in the cyclotomic group of the fifth roots of...

14N20 | Theoretical, Mathematical and Computational Physics | 14G32 | Mathematics | 14H50 | Fundamental group | 14F35 | 14F45 | 32S22 | Line arrangements | Mathematics, general | Applications of Mathematics | Number fields | Zariski pairs | MATHEMATICS | VARIETIES | CONJUGATE

14N20 | Theoretical, Mathematical and Computational Physics | 14G32 | Mathematics | 14H50 | Fundamental group | 14F35 | 14F45 | 32S22 | Line arrangements | Mathematics, general | Applications of Mathematics | Number fields | Zariski pairs | MATHEMATICS | VARIETIES | CONJUGATE

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 6/2012, Volume 158, Issue 1, pp. 235 - 259

A series of Zariski pairs and three Zariski triplets were found by using lattice theory of K3 surfaces. Explicit equations for typical ones were calculated.

Geometry | Zariski pair | 14J28 | Mathematics | 14H50 | Sextic curve | Simple singularity | 14F45 | MATHEMATICS

Geometry | Zariski pair | 14J28 | Mathematics | 14H50 | Sextic curve | Simple singularity | 14F45 | MATHEMATICS

Journal Article

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