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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
Journal Article
Dover books on advanced mathematics, S336, x, 201 p. diagrs.
Book
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
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
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
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
Journal Article
1986, ISBN 9780387963716, Volume 111., xv, 350
Book
1962, Dover books on advanced mathematics, Volume S336., 201
Book
1950, Princeton mathematical series, Volume no. 13, 201
Book
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
Journal Article
1962, Dover books on advanced mathematics, S336, x, 201 p. diagrs.
Book
1950, ISBN 0387903615, Volume 13.
Book
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
Journal Article
1992, Mathematical notes, ISBN 0691085595, Volume 40., xv, 427
Book
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
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
Book
manuscripta mathematica, ISSN 0025-2611, 5/2018, Volume 156, Issue 1, pp. 137 - 147
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
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
Book
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