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Fixed obvious typos and rearranged some of the grammar.
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Sam Nead
Sam Nead
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Assume we have a surface $S$ (smooth if you want), and a map $f: S \to V$ that contracts a a curve $C \subset S$. What What condition would give a factoring of $f$ through a contraction $c : V \to V'$ $c: S \to V'$ contracting $X$ and is isomorphic$C$ but otherwise being an isomorphism?

What about the special case where $S$ is a flat family of curves and $X$$C$ is the central fiber (all other fibers are assumed smooth). What criterion would give a factoring of $f$ through the the contraction?

Assume we have a surface $S$ (smooth if you want), and a map $f: S \to V$ that contracts a curve $C \subset S$. What condition would give a factoring of $f$ through a contraction $c : V \to V'$ contracting $X$ and is isomorphic otherwise?

What about the special case where $S$ is a flat family of curves and $X$ is the central fiber (all other fibers are assumed smooth). What criterion would give a factoring of $f$ through the contraction?

Assume we have a surface $S$ (smooth if you want), and a map $f: S \to V$ that contracts a curve $C \subset S$. What condition would give a factoring of $f$ through a contraction $c: S \to V'$ contracting $C$ but otherwise being an isomorphism?

What about the special case where $S$ is a flat family of curves and $C$ is the central fiber (all other fibers are assumed smooth). What criterion would give a factoring of $f$ through the contraction?

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Tmonk
Tmonk
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Contraction of curves on surfaces

Assume we have a surface $S$ (smooth if you want), and a map $f: S \to V$ that contracts a curve $C \subset S$. What condition would give a factoring of $f$ through a contraction $c : V \to V'$ contracting $X$ and is isomorphic otherwise?

What about the special case where $S$ is a flat family of curves and $X$ is the central fiber (all other fibers are assumed smooth). What criterion would give a factoring of $f$ through the contraction?