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Results tagged with birational-geometry
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user 46104
Birational geometry is a field of algebraic geometry the goal of which is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles.
2
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Accepted
Is each rationally chain connected surface rational?
By the comments of abx you only need an answer to question $3$. You get easily an answer if you assume the results in the classical book of Beauville on algebraic surfaces.
Namely, if $S$ is uniruled …
- 1,054
1
vote
Automorphisms of Cartesian products
This is true under the assumption you suggest, $X$ of general type, when $X$ is a curve.
In the simplest case $r=2$, Corollary 3.9 of this paper of Catanese gives that $Aut(X^2)$ is the semidirect pr …
- 1,054
2
votes
Classification of quartic surfaces
A fine classification of the quartic surfaces that are not normal is in
Tohsuke URABE, "Classification of Non-normal Quartic Surfaces", TOKYO J. MATH. VOL. 9, No. 2, 1986, 265-295
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