Examples
- The moduli space of algebraic curves (Deligne–Mumford stack) defined as a universal family of curves of given genus g does not exist as a fine moduli space as an algebraic variety because in particular there are elliptic curves admitting nontrivial automorphisms (though there is an algebraic variety forming a coarse moduli space). For elliptic curves over the complex numbers the corresponding stack is a quotient of the upper half-plane by the action of the modular group.
Read more about this topic: Algebraic Stack
Famous quotes containing the word examples:
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)