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Results tagged with complex-geometry
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user 8621
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.
6
votes
Accepted
Elliptic fibrations with few singular fibers
Consider first an elliptic fibration with a section over $\mathbb{P}^1$. (In this case none of the singular fibers are multiples of smooth curves.)
Assume that the minimal discriminant has degree $12 …
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1
vote
Accepted
Infinitely many rational nt multisection in elliptic K3 surfaces by deformation theory
Question 1: $S'$ is an elliptic surface without a section such that it is Jacobian is $S$. The surfaces with this property are parametrized by a certain cohomology group and the cocycle the authors re …
- 3,338
3
votes
Automorphisms of generic complete intersections
You may try the following:
I believe (I did not check the details) that the monodromy representation on the primitive part of $H^n(X,\mathbb{C})_{prim}$ is irreducible, as in the case of hypersurface …
- 3,338
1
vote
The locus of rational/elliptic curves on a special surface in $\mathbb{P}^3$
There are results by Voisin (On a conjecture of Clemens on rational curves on hypersurfaces Journal of Differential Geometry 44 (1996) 200-214) and Ulmer (Rational curves on elliptic surfaces, arXiv:1 …
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2
votes
$b_2$ of the blow up of a complex $3$-fold in a curve
I am not sure whether $b_2(V')-b_2(V)=1$ always holds. Anyway, in the book of Peters and Steenbrink you can find "the Mayer-Vietoris sequence of the discriminant square". If $E$ is the exceptional div …
- 3,338
2
votes
Number of Elliptic fiberation
This question is highly non-trivial. The usual strategy is too determine the N\'eron-Severi lattice of $X$, determine all effective -2 curves and then determine all possible divisors $F$ consisting of …
CommunityBot
- 1
5
votes
Reference for elliptic 3-folds
Rick Miranda's text (mentioned by Artie) describes how one can obtain an elliptic threefold from a Weierstrass equation and how the singular fibers behave in the particular model he constructed. (In t …
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