There Are No Projective Surfaces in M 4
نویسنده
چکیده
We answer the first non-classical case of a question of J. Harris from the 1983 ICM: what is the largest possible dimension of a complete subvariety of Mg ? Working over a base field with characteristic 0 or greater then 3 we prove that there are no projective surfaces in the moduli space of curves of genus 4; thus proving that the largest possible dimension of a projective subvariety in M4 is 1.
منابع مشابه
On two generalizations of semi-projective modules: SGQ-projective and $pi$-semi-projective
Let $R$ be a ring and $M$ a right $R$-module with $S=End_R(M)$. A module $M$ is called semi-projective if for any epimorphism $f:Mrightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: Mrightarrow N$, there exists $h:Mrightarrow M$ such that $fh=g$. In this paper, we study SGQ-projective and $pi$-semi-projective modules as two generalizations of semi-projective modules. A ...
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تاریخ انتشار 2008