Publications of the Research Institute for Mathematical Sciences, ISSN 0034-5318, 2018, Volume 54, Issue 1, pp. 163 - 179

We define a class of plane curves that are close to the free divisors in terms of the local cohomology of their Jacobian algebras and such that, conjecturally, any rational cuspidal curve C is either...

Rational cuspidal curve | Jacobian ideal | Milnor algebra | Free divisor | MATHEMATICS | LINE ARRANGEMENTS | rational cuspidal curve

Rational cuspidal curve | Jacobian ideal | Milnor algebra | Free divisor | MATHEMATICS | LINE ARRANGEMENTS | rational cuspidal curve

Journal Article

2013, Annals of mathematics studies, ISBN 9780691155913, Volume no. 184, viii, 256

This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series...

Automorphic forms | Quaternions | Arithmetical algebraic geometry | Shimura varieties | Mathematics | PBH | Number Theory

Automorphic forms | Quaternions | Arithmetical algebraic geometry | Shimura varieties | Mathematics | PBH | Number Theory

Book

Journal of algebra, ISSN 0021-8693, 2019, Volume 519, pp. 474 - 490

We give an efficient algorithm to compute equations of twists of hyperelliptic curves C of arbitrary genus over any perfect field k...

Hyperelliptic curves | Twists | Conics | Galois cohomology | MATHEMATICS | Hyperclliptic curves | Algorithms | Mathematics - Number Theory | Mathematics | Number Theory

Hyperelliptic curves | Twists | Conics | Galois cohomology | MATHEMATICS | Hyperclliptic curves | Algorithms | Mathematics - Number Theory | Mathematics | Number Theory

Journal Article

2008, ISBN 9780521771948, Volume 9780521771948, xix, 543

Book

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2019, Volume 371, Issue 9, pp. 6377 - 6402

.... We determine explicitly the jumps of the ramification filtrations in terms of pole numbers. We give applications for curves with zero p-rank...

ARTIN-SCHREIER EXTENSIONS | REPRESENTATIONS | big actions | Harbater-Katz-Gabber covers | zero p-rank | P-GROUP | Automorphisms | MODULI | numerical semigroups | COMPOSITUM | MATHEMATICS | curves | ALGEBRAIC FUNCTION | LOCAL LIFTING PROBLEM | DIFFERENTIALS | Galois module structure | POINTS | RAMIFICATION

ARTIN-SCHREIER EXTENSIONS | REPRESENTATIONS | big actions | Harbater-Katz-Gabber covers | zero p-rank | P-GROUP | Automorphisms | MODULI | numerical semigroups | COMPOSITUM | MATHEMATICS | curves | ALGEBRAIC FUNCTION | LOCAL LIFTING PROBLEM | DIFFERENTIALS | Galois module structure | POINTS | RAMIFICATION

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2016, Volume 368, Issue 10, pp. 7019 - 7043

Let S be a Dedekind scheme with field of functions K. We show that if X-K is a smooth connected proper curve of positive genus over K, then it admits a Neron model over S, i.e...

MATHEMATICS | Neron model | curve | good reduction | Algebraic Geometry | Mathematics

MATHEMATICS | Neron model | curve | good reduction | Algebraic Geometry | Mathematics

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2019, Volume 88, Issue 315, pp. 421 - 438

Given a smooth curve defined over a field k that admits a non-singular plane model over \overline {k...

Automorphism groups | Twist | Non-singular plane curves | HYPERELLIPTIC CURVES | MATHEMATICS, APPLIED | automorphism groups | twist | Algebraic Geometry | Mathematics | Number Theory

Automorphism groups | Twist | Non-singular plane curves | HYPERELLIPTIC CURVES | MATHEMATICS, APPLIED | automorphism groups | twist | Algebraic Geometry | Mathematics | Number Theory

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2019, Volume 88, Issue 318, pp. 1913 - 1927

We give an algorithm to compute the conductor for curves of genus 2. It is based on the analysis of 3-torsion of the Jacobian for genus 2 curves over 2-adic...

Hyperelliptic curves | Local fields | 3-torsion | Conductor | FIELDS | MATHEMATICS, APPLIED | hyperelliptic curves | local fields | JACOBIANS

Hyperelliptic curves | Local fields | 3-torsion | Conductor | FIELDS | MATHEMATICS, APPLIED | hyperelliptic curves | local fields | JACOBIANS

Journal Article

Duke mathematical journal, ISSN 0012-7094, 2013, Volume 162, Issue 10, pp. 1877 - 1894

We study curves of negative self-intersection on algebraic surfaces. In contrast to what occurs in positive characteristics, it turns out that any...

MATHEMATICS | PROPORTIONALITY | Mathematics - Algebraic Geometry | 14C17 | 14G35

MATHEMATICS | PROPORTIONALITY | Mathematics - Algebraic Geometry | 14C17 | 14G35

Journal Article

2010, 2nd ed., Graduate texts in mathematics, ISBN 0387094938, Volume 106., xx, 513

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study...

Curves, Elliptic | Curves, Algebraic | Arithmetic | Algebraic Geometry | Mathematics | Algebra | Number Theory

Curves, Elliptic | Curves, Algebraic | Arithmetic | Algebraic Geometry | Mathematics | Algebra | Number Theory

Book

manuscripta mathematica, ISSN 0025-2611, 5/2018, Volume 156, Issue 1, pp. 137 - 147

...–Noether space curve passes.

Geometry | Topological Groups, Lie Groups | 14H60 | Calculus of Variations and Optimal Control; Optimization | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 14H50 | MATHEMATICS

Geometry | Topological Groups, Lie Groups | 14H60 | Calculus of Variations and Optimal Control; Optimization | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 14H50 | MATHEMATICS

Journal Article

Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 02/2019, Volume 2019, Issue 747, pp. 147 - 174

Let be a complex rational cuspidal curve and let be the minimal log resolution of singularities...

MATHEMATICS | Mathematics - Algebraic Geometry

MATHEMATICS | Mathematics - Algebraic Geometry

Journal Article

2007, The Cambridge monographs on applied and computational mathematics, ISBN 0521863708, Volume 23, xiii, 214

Many applications in science and engineering require a digital model of a real physical object. Advanced scanning technology has made it possible to scan such...

Curves on surfaces | Surfaces | Mathematical models | Surfaces, Models of

Curves on surfaces | Surfaces | Mathematical models | Surfaces, Models of

Book

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