Philip Engel
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Registered User
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May 15 |
awarded | ● Supporter |
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May 14 |
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Magic trick based on deep mathematics Haha, my friend and I barely managed to work through the logic with the audience choosing the numbers 2 and 3! |
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May 1 |
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Complete curves in $M_g$ and Theta Characteristics Thanks for the reference, this is exactly what I was looking for. |
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May 1 |
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Enriques classification of algebraic surfaces One direct way to show $\kappa(S)=-\infty$ implies $S$ is ruled is to use Iitaka's Conjecture: If $S$ is a surface and $S\rightarrow B$ is a fibration with generic fiber $F$ then $\kappa(S)\geq\kappa(B)+\kappa(F)$. Applying this to the Albanese fibration solves case (2) above instantaneously, because it implies that $F$ must be rational. This applies the stronger assumption $P_n=0$ for all $n$ rather than $P_{12}=0$ though. I think there really will be no way to get the specific number $12$ without some classification. |
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Apr 30 |
revised |
Enriques classification of algebraic surfaces added 23 characters in body; added 47 characters in body |
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Apr 30 |
answered | Enriques classification of algebraic surfaces |
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Apr 30 |
asked | Complete curves in $M_g$ and Theta Characteristics |
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Apr 22 |
awarded | ● Disciplined |
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Mar 6 |
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Contracting a curve of negative self-intersection on a surface Thanks for your answer, it partially resolves the case of my second question, by giving criteria for contractibility in the algebraic category in certain cases. I mainly wanted an explicit construction {\it in the analytic category} of the contraction. (The conditions would of course be weaker if we allow the contraction not to be an algebraic surface). Since the proposition above seems to be the best result about contractibility, I assume it is hard then to determine whether the resulting surface is algebraic... |
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Mar 1 |
asked | Contracting a curve of negative self-intersection on a surface |
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Feb 19 |
awarded | ● Necromancer |
