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Results tagged with complex-geometry
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user 6107
Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
8
votes
Accepted
Homogeneous polynomials cutting out complex abelian varieties
Horrocks-Mumford surfaces are cut out in ${\mathbb P}^4$ by 3 quintic and 15 sextic polynomials; the equations will have many dependencies (syzygies) between them. The references I found are [Manolach …
- 3,202
1
vote
Locally affine varieties and du Val singularities
A chapter of the unpublished PhD thesis of Rebecca Leng, a student of Miles Reid from about 2002, presents a careful study of a natural affine cover of the minimal resolution $Y={\rm GHilb}({\mathbb A …
- 3,202
4
votes
References for Riemann surfaces
I am copying this here from the official CUP website, so I don't think I am breaching anyone's copyright: a short review of one of my old favourites; seems to address precisely the points you are inte …
1
vote
Lattice polarized K3 surfaces
Let me add one more, slightly different perspective: the notion of lattice polarization for K3s becomes very natural from the point of view of families of higher-dimensional Calabi-Yau manifolds. If $ …
- 3,202
1
vote
Question on Kähler/ample cone, cone of curves....
There is an interesting special case when the answer to your Question 4 is positive. Assume that $X$ is a smooth fourfold, and $Y$ an ample anticanonical hypersurface (in particular then $X$ is Fano a …
- 3,202