### Some open problems in computational algebraic geometry.

*T. Shaska*

#### Abstract

The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems of computational algebraic geometry which can be approached from a computational viewpoint. Such problems are the decomposition of Jacobians of genus two curves, automorphisms groups of algebraic curves and the corresponding loci in $\mathcal M_g$, inclusions among such loci, decomposition of Jacobians of algebraic curves with automorphisms, invariants of binary

forms, monodromy group of a generic curve covering $\mathbb P^1$, field of moduli versus field of definition of curves, theta functions of curves with automorphisms, etc.

forms, monodromy group of a generic curve covering $\mathbb P^1$, field of moduli versus field of definition of curves, theta functions of curves with automorphisms, etc.

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