Journal of Pure and Applied Algebra, ISSN 0022-4049, 01/2020, Volume 224, Issue 1, pp. 272 - 299

We determine which of the modular curves XΔ(N), that is, curves lying between X0(N) and X1(N), are bielliptic. Somewhat surprisingly, we find that one of these...

Bielliptic | Modular curve | Hyperelliptic | Infinitely many quadratic points | COMPACT RIEMANN SURFACES | MATHEMATICS | AUTOMORPHISM-GROUPS | ELLIPTIC-CURVES | MATHEMATICS, APPLIED | TORSION POINTS | GENUS

Bielliptic | Modular curve | Hyperelliptic | Infinitely many quadratic points | COMPACT RIEMANN SURFACES | MATHEMATICS | AUTOMORPHISM-GROUPS | ELLIPTIC-CURVES | MATHEMATICS, APPLIED | TORSION POINTS | GENUS

Journal Article

Acta Arithmetica, ISSN 0065-1036, 2013, Volume 161, Issue 3, pp. 283 - 299

Journal Article

Journal of Number Theory, ISSN 0022-314X, 04/2018, Volume 185, pp. 319 - 338

In this work, we determine all modular curves X0+(N) that are bielliptic, and then find all numbers N for which the curves X0+(N) admit infinitely many...

Quadratic points | Bielliptic | Modular curve

Quadratic points | Bielliptic | Modular curve

Journal Article

Journal of number theory, ISSN 0022-314X, 11/2020, Volume 216, pp. 380 - 402

Journal Article

Journal of algebra, ISSN 0021-8693, 10/2020, Volume 559, pp. 726 - 759

Let N >= 1 be a integer such that the modular curve X-0* (N) has genus >= 2. We prove that X-0* (N) is bielliptic exactly for 69 values of N. In particular, we...

MATHEMATICS | Hyperelliptic curves | Quadratic points | Arithmetic geometry | Elliptic curves | Bielliptic curves | Modular curves | Involutions | GENUS

MATHEMATICS | Hyperelliptic curves | Quadratic points | Arithmetic geometry | Elliptic curves | Bielliptic curves | Modular curves | Involutions | GENUS

Journal Article

Journal of algebra, ISSN 0021-8693, 10/2020, Volume 559, pp. 726 - 759

Let N≥1 be a integer such that the modular curve X0⁎(N) has genus ≥2. We prove that X0⁎(N) is bielliptic exactly for 69 values of N. In particular, we obtain...

Hyperelliptic curves | Quadratic points | Arithmetic geometry | Elliptic curves | Bielliptic curves | Modular curves | Involutions

Hyperelliptic curves | Quadratic points | Arithmetic geometry | Elliptic curves | Bielliptic curves | Modular curves | Involutions

Journal Article

Advances in Mathematics, ISSN 0001-8708, 06/2019, Volume 349, pp. 125 - 161

We study the Hodge structure of elliptic surfaces which are canonically defined from bielliptic curves of genus three. We prove that the period map for the...

Torelli problem | Elliptic surfaces | Bielliptic curves | Prym varieties | MATHEMATICS | GLOBAL TORELLI | THEOREM | GENERAL TYPE | MODULI

Torelli problem | Elliptic surfaces | Bielliptic curves | Prym varieties | MATHEMATICS | GLOBAL TORELLI | THEOREM | GENERAL TYPE | MODULI

Journal Article

Journal of Number Theory, ISSN 0022-314X, 08/2020, Volume 213, pp. 445 - 452

We study the arithmetic (geometric) progressions in the x-coordinates of quadratic points on smooth planar curves defined over a number field k. Unless the...

Smooth plane curves | Quadratic points | Bielliptic curves | Progression sequences | MATHEMATICS | POINTS

Smooth plane curves | Quadratic points | Bielliptic curves | Progression sequences | MATHEMATICS | POINTS

Journal Article

Journal of Algebra, ISSN 0021-8693, 2011, Volume 332, Issue 1, pp. 229 - 243

Let k be an algebraically closed field and let C be a non-hyperelliptic smooth projective curve of genus g defined over k. Since the canonical model of C is...

Curve | Artinian Gorenstein algebra | Bielliptic curve | Apolarity | Almost minimal degree | SYSTEM | MATHEMATICS | MINIMAL DEGREE | SYZYGIES | VARIETIES | POWERS | SUMS

Curve | Artinian Gorenstein algebra | Bielliptic curve | Apolarity | Almost minimal degree | SYSTEM | MATHEMATICS | MINIMAL DEGREE | SYZYGIES | VARIETIES | POWERS | SUMS

Journal Article

Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova, ISSN 0041-8994, 2013, Volume 130, pp. 203 - 213

We prove that the canonical cover of an Enriques surface does not admit non-trivial Fourier-Mukai partners. We also show that the canonical cover of a...

Derived categories | Fourier-Mukai partners | Bielliptic surfaces | Enriques surfaces | bielliptic surfaces | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | Mathematics - Algebraic Geometry

Derived categories | Fourier-Mukai partners | Bielliptic surfaces | Enriques surfaces | bielliptic surfaces | MATHEMATICS | MATHEMATICS, APPLIED | NUMBER | Mathematics - Algebraic Geometry

Journal Article

JOURNAL OF NUMBER THEORY, ISSN 0022-314X, 04/2018, Volume 185, pp. 319 - 338

In this work, we determine all modular curves X-0(+)(N) that are bielliptic, and then find all numbers N for which the curves X-0(+) (N) admit infinitely many...

MATHEMATICS | Quadratic points | ABELIAN-VARIETIES | HECKE OPERATORS | Bielliptic | Modular curve

MATHEMATICS | Quadratic points | ABELIAN-VARIETIES | HECKE OPERATORS | Bielliptic | Modular curve

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2018, Volume 294, Issue 2, pp. 495 - 504

Let [(B) over bar (2,0, 20)] and [B-2,B-0,B- 20] respectively be the classes of the loci of stable and of smooth bielliptic curves with 20 marked points where...

Bielliptic | Nontautological | MATHEMATICS | nontautological | SPACES | bielliptic | COVERS | CURVES | MODULI | TAUTOLOGICAL RING | Mathematics - Algebraic Geometry

Bielliptic | Nontautological | MATHEMATICS | nontautological | SPACES | bielliptic | COVERS | CURVES | MODULI | TAUTOLOGICAL RING | Mathematics - Algebraic Geometry

Journal Article

Contemporary Mathematics, ISSN 0271-4132, 2018, Volume 701, pp. 17 - 34

Conference Proceeding

Journal of Number Theory, ISSN 0022-314X, 09/2017, Volume 178, pp. 1 - 4

Skorobogatov constructed a bielliptic surface which is a counterexample to the Hasse principle not explained by the Brauer–Manin obstruction. We show that this...

Bielliptic surfaces | Zero-cycles | Brauer–Manin obstruction | MATHEMATICS | Brauer Manin obstruction

Bielliptic surfaces | Zero-cycles | Brauer–Manin obstruction | MATHEMATICS | Brauer Manin obstruction

Journal Article

JP Journal of Algebra, Number Theory and Applications, ISSN 0972-5555, 11/2012, Volume 27, Issue 1, pp. 45 - 60

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 2/2008, Volume 131, Issue 1, pp. 111 - 122

Let $${\mathcal{E}}$$ be an ample vector bundle of rank r ≥ 2 on a smooth complex projective variety X of dimension n such that there exists a global section...

Geometry | Fano manifold | 14F05 | 14J45 | Bielliptic curve | 14J40 | Mathematics | 14J60 | Ample vector bundle | MATHEMATICS | ample vector bundle | bielliptic curve | SMALL INVARIANTS | EMBEDDED PROJECTIVE VARIETIES | SURFACES

Geometry | Fano manifold | 14F05 | 14J45 | Bielliptic curve | 14J40 | Mathematics | 14J60 | Ample vector bundle | MATHEMATICS | ample vector bundle | bielliptic curve | SMALL INVARIANTS | EMBEDDED PROJECTIVE VARIETIES | SURFACES

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 03/2016, Volume 220, Issue 3, pp. 1258 - 1279

For any finite abelian group G, we study the moduli space of abelian G-covers of elliptic curves, in particular identifying the irreducible components of the...

SPACE | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | BUNDLES | CYCLIC COVERS | COMPACTIFICATIONS | BIELLIPTIC CURVES | STACKS

SPACE | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | BUNDLES | CYCLIC COVERS | COMPACTIFICATIONS | BIELLIPTIC CURVES | STACKS

Journal Article

Hokkaido Mathematical Journal, ISSN 0385-4035, 2015, Volume 44, Issue 2, pp. 165 - 173

In this paper, we shall prove that if an irreducible curve X of genus 5 over C has 24 Weierstrass points of weight 5, then it has exactly three bielliptic...

Bielliptic involutions | Algebraic curves | Weierstrass points | MATHEMATICS | algebraic curves | bielliptic involutions

Bielliptic involutions | Algebraic curves | Weierstrass points | MATHEMATICS | algebraic curves | bielliptic involutions

Journal Article

European journal of mathematics, ISSN 2199-6768, 2017, Volume 4, Issue 1, pp. 26 - 36

After recalling the definition and basic properties of Ulrich bundles, we focus on the existence problem: does every smooth projective variety carry an Ulrich...

Determinantal hypersurfaces | Abelian surface | Fano threefolds | 14D20 | Bielliptic surface | Algebraic Geometry | Mathematics | 14J60 | Ulrich bundle | Enriques surface

Determinantal hypersurfaces | Abelian surface | Fano threefolds | 14D20 | Bielliptic surface | Algebraic Geometry | Mathematics | 14J60 | Ulrich bundle | Enriques surface

Journal Article

Mathematical Notes, ISSN 0001-4346, 3/2016, Volume 99, Issue 3, pp. 397 - 405

Let S be a bielliptic surface over a finite field, and let an elliptic curve B be the Albanese variety of S; then the zeta function of the surface S is equal...

Mathematics, general | zeta function | bielliptic surface | elliptic curve | Mathematics | finite field | MATHEMATICS

Mathematics, general | zeta function | bielliptic surface | elliptic curve | Mathematics | finite field | MATHEMATICS

Journal Article

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