Transactions of the American Mathematical Society, ISSN 0002-9947, 04/2020, Volume 373, Issue 4, pp. 2913 - 2931

We will prove that there are infinitely many families of K3 surfaces which both admit a finite symplectic automorphism...

MATHEMATICS | quotients | PROJECTIVE MODELS | isogenies between K3 surfaces | K3 surfaces | Galois covers between K3 surfaces | symplectic automorphisms on K3 surfaces | SYMPLECTIC AUTOMORPHISMS

MATHEMATICS | quotients | PROJECTIVE MODELS | isogenies between K3 surfaces | K3 surfaces | Galois covers between K3 surfaces | symplectic automorphisms on K3 surfaces | SYMPLECTIC AUTOMORPHISMS

Journal Article

The Rocky Mountain journal of mathematics, ISSN 0035-7596, 2016, Volume 46, Issue 4, pp. 1141 - 1205

Journal Article

Mathematische Annalen, ISSN 0025-5831, 06/2017, Volume 368, Issue 1-2, pp. 753 - 809

We show that the maximal number of (real) lines in a (real) nonsingular spatial quartic surface is 64 (respectively, 56...

14N25 | Primary 14J28 | Secondary 14J27 | MATHEMATICS | RATIONAL CURVES | K3 SURFACES | Mathematics - Algebraic Geometry

14N25 | Primary 14J28 | Secondary 14J27 | MATHEMATICS | RATIONAL CURVES | K3 SURFACES | Mathematics - Algebraic Geometry

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 2017, Volume 115, Issue 6, pp. 1276 - 1316

...), with elements in the Brauer groups of K3‐surfaces of degree 2, and with Verra threefolds. These hyper‐Kähler fourfolds admit natural involutions and complete the classification of geometric realizations of antisymplectic involutions on hyper...

14D20 | 14D06 | 14J35 (primary) | 14J32 | 14E25 | MATHEMATICS | HYPERKAHLER MANIFOLDS | 4-FOLDS | K3 SURFACES | CUBIC FOURFOLD | EPW-SEXTICS | FORMULAS | mattmatikk

14D20 | 14D06 | 14J35 (primary) | 14J32 | 14E25 | MATHEMATICS | HYPERKAHLER MANIFOLDS | 4-FOLDS | K3 SURFACES | CUBIC FOURFOLD | EPW-SEXTICS | FORMULAS | mattmatikk

Journal Article

COMMENTARII MATHEMATICI HELVETICI, ISSN 0010-2571, 2019, Volume 94, Issue 3, pp. 445 - 458

We prove that isogenous K3 surfaces have isomorphic Chow motives. This provides a motivic interpretation of a long standing conjecture of Safarevic which has been settled only recently by Buskin...

MATHEMATICS | Hodge conjecture | Brauer groups | motives | EQUIVALENCES | derived categories | K3 surfaces | twisted K3 surfaces

MATHEMATICS | Hodge conjecture | Brauer groups | motives | EQUIVALENCES | derived categories | K3 surfaces | twisted K3 surfaces

Journal Article

Journal of Differential Geometry, ISSN 0022-040X, 01/2016, Volume 102, Issue 1, pp. 127 - 172

We prove that the Gromov-Hausdorff compactification of the moduli space of Kahler-Einstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification...

MATHEMATICS | GIT | SINGULARITIES | DEGENERATIONS | STABILITY | GENERALIZED FUTAKI INVARIANT | K3 SURFACES | COMPLEX-SURFACES | CLASSIFICATION | MANIFOLDS | CURVES

MATHEMATICS | GIT | SINGULARITIES | DEGENERATIONS | STABILITY | GENERALIZED FUTAKI INVARIANT | K3 SURFACES | COMPLEX-SURFACES | CLASSIFICATION | MANIFOLDS | CURVES

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2013, Volume 141, Issue 1, pp. 131 - 137

surfaces with Shioda-Inose structure.]]>

K3 surface | Shioda-Inose structure | Rational map | MATHEMATICS | MATHEMATICS, APPLIED | rational map

K3 surface | Shioda-Inose structure | Rational map | MATHEMATICS | MATHEMATICS, APPLIED | rational map

Journal Article

Compositio mathematica, ISSN 0010-437X, 01/2018, Volume 154, Issue 1, pp. 1 - 35

...$ -adic cohomology group of a K3 surface over $K$ implies that the surface has good reduction after a finite and unramified extension...

Galois representations | K3 surfaces | good reduction | MATHEMATICS | ABELIAN-VARIETIES | ENRIQUES | DEGENERATION

Galois representations | K3 surfaces | good reduction | MATHEMATICS | ABELIAN-VARIETIES | ENRIQUES | DEGENERATION

Journal Article

COMPOSITIO MATHEMATICA, ISSN 0010-437X, 05/2019, Volume 155, Issue 5, pp. 912 - 937

Derived equivalences of twisted K3 surfaces induce twisted Hodge isometries between them; that is, isomorphisms of their cohomologies which respect certain natural lattice structures and Hodge structures...

DIFFEOMORPHISMS | MATHEMATICS | deformations | CATEGORY | EQUIVALENCES | derived categories | CURVES | twisted K3 surfaces | twisted Hodge structures | MODULI | Mathematics - Algebraic Geometry

DIFFEOMORPHISMS | MATHEMATICS | deformations | CATEGORY | EQUIVALENCES | derived categories | CURVES | twisted K3 surfaces | twisted Hodge structures | MODULI | Mathematics - Algebraic Geometry

Journal Article

ALGEBRAIC GEOMETRY, ISSN 2313-1691, 07/2019, Volume 6, Issue 4, pp. 410 - 426

We give an explicit construction for the 4-dimensional family of Schoen surfaces by computing equations for their canonical images, which are 40-nodal complete intersections of a quadric and the Igusa quartic in P-4...

MATHEMATICS | PRODUCT | GENERAL TYPE | Segre cubic | K3 surfaces | irregular surfaces | Lagrangian surfaces | Igusa quartic | Algebraic Geometry | Mathematics

MATHEMATICS | PRODUCT | GENERAL TYPE | Segre cubic | K3 surfaces | irregular surfaces | Lagrangian surfaces | Igusa quartic | Algebraic Geometry | Mathematics

Journal Article

COMPOSITIO MATHEMATICA, ISSN 0010-437X, 05/2019, Volume 155, Issue 5, pp. 902 - 911

We give a proof of the formality conjecture of Kaledin and Lehn: on a complex projective K3 surface, the differential graded (DG) algebra RHom(center dot) (F; F...

MATHEMATICS | stable sheaves | REPRESENTATIONS | SINGULARITIES | DG algebras | formality | DG enhancements | STABILITY CONDITIONS | K3 surfaces | BIRATIONAL GEOMETRY | MODULI SPACES | SHEAVES | Geometry | Sheaves | Algebra | Symmetry

MATHEMATICS | stable sheaves | REPRESENTATIONS | SINGULARITIES | DG algebras | formality | DG enhancements | STABILITY CONDITIONS | K3 surfaces | BIRATIONAL GEOMETRY | MODULI SPACES | SHEAVES | Geometry | Sheaves | Algebra | Symmetry

Journal Article

Advances in Mathematics, ISSN 0001-8708, 08/2016, Volume 298, pp. 369 - 392

We study threefolds fibred by mirror quartic K3 surfaces. We begin by showing that any family of such K3 surfaces is completely determined by a map from the base of the family to the moduli space of mirror quartic K3 surfaces...

K3 surface | Fibration | Calabi–Yau threefold | Calabi-Yau threefold | MATHEMATICS | Mathematics - Algebraic Geometry

K3 surface | Fibration | Calabi–Yau threefold | Calabi-Yau threefold | MATHEMATICS | Mathematics - Algebraic Geometry

Journal Article

Journal of Differential Geometry, ISSN 0022-040X, 2014, Volume 97, Issue 1, pp. 149 - 175

Catanese surfaces are regular surfaces of general type with p(g) = 0. They specialize to double covers of Barlow surfaces...

MATHEMATICS | K3 SURFACES | RATIONAL EQUIVALENCE | VARIETIES | GENERAL TYPE | ZERO CYCLES | PG=0 | Algebraic Geometry | Mathematics

MATHEMATICS | K3 SURFACES | RATIONAL EQUIVALENCE | VARIETIES | GENERAL TYPE | ZERO CYCLES | PG=0 | Algebraic Geometry | Mathematics

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 2014, Volume 163, Issue 13, pp. 2357 - 2425

Given a K3 surface X over a field of characteristic p. Artin conjectured that if X is supersingular...

FORMS | MATHEMATICS | ABELIAN-VARIETIES | REPRESENTATIONS | EXTENDING FAMILIES | SINGULARITIES | CURVES | MODULI | CONJECTURE | Kuga–Satake varieties | Tate conjecture | 14G15 | 14J28 | semistable reduction | Borcherds products | supersingular varieties | K3 surfaces

FORMS | MATHEMATICS | ABELIAN-VARIETIES | REPRESENTATIONS | EXTENDING FAMILIES | SINGULARITIES | CURVES | MODULI | CONJECTURE | Kuga–Satake varieties | Tate conjecture | 14G15 | 14J28 | semistable reduction | Borcherds products | supersingular varieties | K3 surfaces

Journal Article

New York Journal of Mathematics, ISSN 1076-9803, 2019, Volume 25, pp. 168 - 173

In this paper, we study the Severi variety V-L,V-g of genus g curves in vertical bar L vertical bar on a general polarized K3 surface (X, L...

K3 surface | Moduli space of curves | Severi variety | MATHEMATICS | severi variety | RATIONAL CURVES | moduli space of curves

K3 surface | Moduli space of curves | Severi variety | MATHEMATICS | severi variety | RATIONAL CURVES | moduli space of curves

Journal Article

Advances in Mathematics, ISSN 0001-8708, 06/2017, Volume 313, pp. 718 - 745

In this paper, we study A1 curves on log K3 surfaces. We classify all genuine log K3 surfaces of type II which admit countably infinite A1 curves.

K3 surface | Rational curves | Log varieties

K3 surface | Rational curves | Log varieties

Journal Article

ALGEBRA & NUMBER THEORY, ISSN 1937-0652, 2019, Volume 13, Issue 6, pp. 1443 - 1454

We show that any polarized K3 surface supports special Ulrich bundles of rank 2.

MATHEMATICS | Ulrich sheaves | ACM BUNDLES | K3 surfaces | ACM vector sheaves and bundles | SHEAVES | MODULI

MATHEMATICS | Ulrich sheaves | ACM BUNDLES | K3 surfaces | ACM vector sheaves and bundles | SHEAVES | MODULI

Journal Article

Compositio mathematica, ISSN 0010-437X, 07/2018, Volume 154, Issue 7, pp. 1508 - 1533

We exhibit a Cremona transformation of $\mathbb{P}^{4}$ such that the base loci of the map and its inverse are birational to K3 surfaces...

K3 surfaces | Cremona transformations | derived equivalences | MATHEMATICS | Mathematics - Algebraic Geometry

K3 surfaces | Cremona transformations | derived equivalences | MATHEMATICS | Mathematics - Algebraic Geometry

Journal Article

Advances in Mathematics, ISSN 0001-8708, 03/2017, Volume 309, pp. 624 - 654

We consider modular properties of nodal curves on general K3 surfaces. Let Kp be the moduli space of primitively polarized K3 surfaces (S,L) of genus p⩾3 and Vp,m,δ...

Moduli map | Moduli spaces of K3 surfaces | Degenerations | Moduli of curves | Severi varieties | Deformation theory | GAUSSIAN MAPS | MATHEMATICS | RATIONAL CURVES

Moduli map | Moduli spaces of K3 surfaces | Degenerations | Moduli of curves | Severi varieties | Deformation theory | GAUSSIAN MAPS | MATHEMATICS | RATIONAL CURVES

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 2017, Volume 166, Issue 1, pp. 75 - 124

We give a complete description of the group of exact autoequivalences of the bounded derived category of coherent sheaves on a K3 surface of Picard rank 1...

SPACE | MATHEMATICS | STABILITY CONDITIONS | CATEGORY | AUTOEQUIVALENCES | Mathematics - Algebraic Geometry

SPACE | MATHEMATICS | STABILITY CONDITIONS | CATEGORY | AUTOEQUIVALENCES | Mathematics - Algebraic Geometry

Journal Article

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