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RECURSIONS FOR CHARACTERISTIC NUMBERS OF GENUS ONE PLANE CURVES
CHARACTERISTIC PLANE CURVES
2015/7/14
Characteristic numbers of families of maps of nodal curves to P2 are de ned as
intersection of natural divisor classes. (This de nition agrees with the usual de nition for
families of plane curves.)...
GENUS 0 AND 1 HURWITZ NUMBERS: RECURSIONS, FORMULAS, AND GRAPH-THEORETIC INTERPRETATIONS
RECURSIONS FORMULAS GRAPH-THEORETIC
2015/7/14
We derive a closed-form expression for all genus 1 Hurwitz numbers, and give a
simple new graph-theoretic interpretation of Hurwitz numbers in genus 0 and 1. (Hurwitz
numbers essentially count irred...
ON ADDING A LIST OF NUMBERS (AND OTHER ONE-DEPENDENT DETERMINANTAL PROCESSES)
Add list of Numbers the determinant processes
2015/7/8
ON ADDING A LIST OF NUMBERS (AND OTHER ONE-DEPENDENT DETERMINANTAL PROCESSES)。
Inspired by this, for the rational
function field K = κ(u) over any finite field κ with characteristic 6= 2, we construct an
explicit 2-parameter family Ec,d of non-isotrivial elli...
No strength in numbers（图）
numbers No strength
2014/3/21
Urban legislators have long lamented that they do not get their fair share of bills passed in state governments, often blaming rural and suburban interests for blocking their efforts. Now, a new study...
Generalization of Proth's and Miller's theorems for $Kp^n+1$ numbers
Proth's Miller's theorems
2010/11/24
In this paper we generalize classical results by Miller and Proth for integers of the form $N=Kp^n+1$. The first generalization of Proth's theorem requires the use of a base which is a $p$-th power n...
We characterize planar diagrams which may be divided into n arc embeddings in terms of their chord diagrams, generalizing a result of Taniyama for the case n = 2. Two algorithms are provided, one whi...
The Atiyah conjecture predicts that the L2-Betti numbers of a finite CW-complex with torsion-free fundamental group are integers. We show that the Atiyah conjecture holds (with an additional technica...
Drawing with Complex Numbers
Drawing Complex Numbers
2010/10/29
It is not commonly realized that the algebra of complex numbers can be used in an elegant way to represent the images of ordinary 3-dimensional figures, orthographically projected to the plane. We de...
Simple Divisibility Rules for the 1st 1000 Prime Numbers
Simple Divisibility Rules 1st 1000 Prime Numbers
2010/10/29
Simple divisibility rules are given for the 1st 1000 prime numbers.