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Mathematician, researching in Algebraic Geometry and related topics.


2d
answered Enriques classification of algebraic surfaces in characteristic zero
May
22
revised K3 surface as an anticanonical section
edited body
May
22
revised K3 surface as an anticanonical section
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May
22
comment K3 surface as an anticanonical section
If $S \subset V$ is not ample, Lefschetz Hyperplane Theorem in general fails and so, at least in principle, we have no control on the Picard number of $V$, even if the Picard number of $S$ is $1$. This makes the question quite tricky.
May
22
revised K3 surface as an anticanonical section
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May
21
comment K3 surface as an anticanonical section
I added this question at the end of my answer.
May
21
revised K3 surface as an anticanonical section
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May
21
comment K3 surface as an anticanonical section
Is there any example of a smooth K3 surface $S$ appearing as a non-ample anticanonical divisor in a smooth $3$-fold?
May
21
comment Preprint by Wall on Sjogren's theorem
You are right. I meant some "unofficial" repositories. Unfortunately, I cannot post the link here without violating the copyright :-)
May
21
revised K3 surface as an anticanonical section
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May
21
comment K3 surface as an anticanonical section
Sorry, you are right. I misread the question, and I have only proved that $S$ cannot be a hyperplane section of a threefold (in this case the threefold is clearly Fano).
May
21
comment K3 surface as an anticanonical section
By adjunction formula $$(K_V+S)|_S = K_S = \mathcal{O}_S,$$ hence $K_V=-$hyperplane class.
May
21
revised K3 surface as an anticanonical section
added 183 characters in body
May
21
answered K3 surface as an anticanonical section
May
21
revised Preprint by Wall on Sjogren's theorem
edited body
May
21
answered Preprint by Wall on Sjogren's theorem
May
21
revised The dualizing sheaf for a proper smooth variety
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May
21
answered The dualizing sheaf for a proper smooth variety
May
19
revised Adjunction map for projective surfaces
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May
19
comment double integral
please do not answer off-topic questions