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AFAIK, these are know only up to genus 3. Genus 2: Igusa (classical). Hyperelliptic genus 3: Shioda (classical). Non hyperelliptic genus 3: a decade ago by Dixmier & Ohno - see https://www.win.tue.n …

If the differences between the spaces starts in codimension 2, then the nerves of the chech coverings (for any reasonable topos you choose) are different in dimensions 2 and up.

There is a nice computational perspective in Bayer and Mumford's What Can Be Computed in Algebraic Geometry? pages 4,5.

No, there is no such $S$: EDIT: (BIG) GAP BELOW I compute limits of certain linear series in the Hurwitz scheme, and then I make claims about limits of other (bigger) linear systems taken over curves …

I assume that by similarity you mean some generalization of the Eucilidean similarity concept, where two shapes are similar if you can map one to the other using a composition of a rigid transformatio …

Regarding EGA, I think the most appropriate answer is: "wy bother ?". Unless you have a really special interest, you shouldn't. Edit Expanding on this (it seems a lot of people seems it's just flame …

As for the first question, the class of X has to be the product of the Chern roots of the bundle, so in the Chow ring, it is the class of a complete intersection. As for the second question, you woul …

you might be looking for Kollar's book Lectures on Resolution of Singularities

In Alain Roberts "Elliptic curves: notes from postgraduate lectures given in Lausanne 1971/72" page 11 (available on google books unless you already tried to read another chapter), there is a hand dra …

Any odd theta characteristic is realized in the canonical system as a hyperplane (dualizing system if you want to work on the boundary too). So, for each curve you get a set of N=(2^g-1)(2^(g-1)) poin …

deg D=2g-2, l(D)=g => D=K deg D=1, l(D) = 2 => g=0 If you want a nice purely geometric fact, deduced from purely numerical arguments, look at Griffiths and Harris p. 258 where they show that a ca …

I don't know how elementary this is, but Igor Dolgachev's online classical algebraic geometry book contains many exercises, as does the first chapter of "Geometry of algebraic ruves" (this whole book …

The proof is actually extremley geometric, if you just wave your hand hard enough. Take an r-dimension variety V in P^{r+d}. Pick a generic point Q in P^{r+d} (where d > 1), and project P^{r+d} from t …

If you fix the 2-torsion points, then all you have is the x->-x involution; so Z/2 times SP_2g(2) is a bound from above. On the other hand, if you take A to be g-fold "power" of some elliptic curve, I …

Under (the extension of) Torrelli this curves maps to one point in Ag. On the other hand the hodge class on Mg minus D0 is a pullback (under the extension of Torelli) of the hodge class on Ag.