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from sage.schemes.chow.all import * | |
# dimension 6 | |
X = ChowScheme(6, ["c2", "c4", "c6"], [2, 4, 6]) | |
X.chowring().inject_variables() | |
td = Sheaf(X, 6, 1 + sum(X.gens())).todd_class() | |
integrand = (td._logg()/2)._expp().by_degrees()[6] | |
# O'Grady 6 | |
values = {c2^3: 30720, c2*c4: 7680, c6: 1920} |
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\documentclass[12pt]{standalone} | |
\usepackage{tikz-cd} | |
\usetikzlibrary{decorations.markings} | |
\makeatletter | |
\tikzcdset{ | |
open/.code={\tikzcdset{hook, circled};}, | |
closed/.code={\tikzcdset{hook, slashed};}, | |
open'/.code={\tikzcdset{hook', circled};}, | |
closed'/.code={\tikzcdset{hook', slashed};}, | |
circled/.code={\tikzcdset{markwith={\draw (0,0) circle (.375ex);}};}, |
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import itertools | |
def reduce(Q): | |
return tuple([qi / gcd(Q) for qi in Q]) | |
def normalise(Q): | |
Q = reduce(Q) | |
D = [gcd(Q[:i] + Q[i+1:]) for i in range(len(Q))] | |
A = [lcm(D[:i] + D[i+1:]) for i in range(len(Q))] | |
a = lcm(A) |
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def genus(degrees): | |
n = len(degrees) + 1 | |
return 1 + 1 / 2 * prod(degrees) * (sum(degrees) - n - 1) | |
""" | |
Generate a list of all genera of complete intersection curves up to a cutoff | |
Observe that the genus strictly increases if we increase the degree of a | |
defining equation, while adding a hyperplane section keeps the degree fixed. | |
So we can obtain all low genera starting from the line in P^2, and increasing |
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# TODO write code |
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def mA(n): | |
if n % 2 == 1: return (n - 1) / 2 | |
else: return (n - 2) / 2 | |
def mD(n): | |
if n % 2 == 1: return (n - 3) / 2 | |
else: return (n - 2) / 2 | |
def u(n): | |
if n % 2 == 1: return mD(n) + 1 |
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# determine the linear equation of a hypersurface under the d-uple embedding | |
def getLinearEquation(equation): | |
d = equation.degree() | |
monomials = getMonomials(equation.parent(), d) | |
coefficients = [equation.monomial_coefficient(monomial) for monomial in monomials] | |
ring = PolynomialRing(QQ, 'x', len(coefficients)) | |
return sum(c * x for c, x in zip(coefficients, ring.gens())) | |
# determine the maximum degree of a list of (homogeneous) equations |
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\documentclass[10pt,a4paper,landscape]{article} | |
\usepackage[T1]{fontenc} | |
\usepackage{amsmath, amsfonts} | |
\usepackage[charter]{mathdesign} | |
\usepackage[scaled]{beramono,berasans} | |
\usepackage{ifthen} | |
\usepackage{tikz} | |
\usetikzlibrary{decorations.pathmorphing, arrows} | |
\begin{document} |
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*.aux | |
*.glo | |
*.idx | |
*.log | |
*.toc | |
*.ist | |
*.acn | |
*.acr | |
*.alg | |
*.bcf |