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Computer Aided Algebraic Geometry

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Surfaces isogenous to a product<br />

<strong>Computer</strong><br />

<strong>Aided</strong><br />

<strong>Algebraic</strong><br />

<strong>Geometry</strong><br />

R. Pignatelli<br />

Surfaces<br />

Invariants<br />

A surface is isogenous to a (higher) product if<br />

S = (C 1 × C 2 )/G where C i are Riemann Surfaces of genus<br />

g i ≥ 2 and G is a group acting freely; S is automatically<br />

minimal of general type with K 2 = 8χ.<br />

Quasi-étale<br />

quotients<br />

Definitions<br />

Computing<br />

invariants<br />

<strong>Computer</strong><br />

Calculations<br />

The Algorithms<br />

Classification<br />

Results<br />

Open<br />

Problems<br />

7 / 19

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