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arithmetic del Pezzo surfaces in comparison with del Pezzo surfaces over a field

A del Pezzo surface is a smooth, 2-dimensional projective variety $X$ with ample anticanonical divisor, i.e. a 2-dimensional Fano variety. I am interested in the arithmetic analogue, a 2-dimensional ...
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1 vote
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117 views

Quotient of K3 surface: complex vs positive characteristic

Let $f: X \to X$ be a non-symplectic automorphism of finite order of complex projective K3 surface $X$. (Recall: Non-symplectic means that the induced action on $H(X,K_X)=H^0(X, \Omega_X^2)$ is not ...
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219 views

Quotient of K3 surfaces by non-symplectic automorphism of finite order

Let $X$ be a $K3$ surface and $f: X \to X$ a non-symplectic morphism (ie non symplectic in sense of that that the induced action on $H(X,K_X=H^0(X, \Omega_X^2)$ is not trivial) of finite order. ...
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Special elliptic pencil of an Enriques surface (arguments in a proof)

I have a couple of questions about arguments in the proof of Lemma 2.6 (see absol page 199, rel p 9) from Shigeyuki Kondo's paper Enriques surfaces with finite automorphism groups: The setup: Let $Y$ ...
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1 vote
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155 views

Sheaf of Kähler Differentials is Invertible in Dense Open Subset

Let $f:S→B$ be an elliptic fibration from an integral surface $S$ to integral curve $B$ . Here I use following definitions: A surface (resp. curve) is a $2$ -dim (resp. $1$-dim) proper k scheme ...
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Irregularity of surfaces for dominant maps

I have a question about an argument in the proof of Lemma 1.2.(1) in Quotients of K3 surfaces modulo involutions by D. Q. Zhang: Let Let $(X, \sigma)$ be X be a smooth projective K3 surface with an ...
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Quotients of K3 surfaces vs cyclic covers

Let $X$ be an algebraic K3 surface (for sake of simplicity, with base field of char $\neq 2$) and $f: X \to X$ a non-symplectic morphism (i.e. non-symplectic in sense of that that the induced action ...
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110 views

Lefschetz Theorem in Dolgachev's On automorphisms of Enriques Surfaces

Let $F$ be a Enriques surface over $\Bbb C$. I have a question about a detail in the proof of Proposition 2.1. from Dolgachev's On automorphisms of Enriques surfaces. This 2.1. Proposition. states ...
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Relative minimal models of pencils of surfaces

I would like to ask for recomendation for literature on theory relative minimal models of surfaces, where "relative" in sense of that the study objects are not surfaces alone (="absolue ...
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-1 votes
1 answer
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Restriction of a Cartier divisor

Let $X$ be a surface (so $2$-dimensional proper $k$-scheme) $D \subset X$ an effective Cartier divisor of $X$ which corresponding to an invertible sheaf $\mathcal{L}=O_X(D)$ and $C \subset X$ a closed ...
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