Conjecture on explicit defining equations for explicit varieties

Let WW be an explicit variety, and distinguish explicit close-to-defining equations from explicit defining equations as in the source. Explicit equations conjecture.

(a) Any explicit variety has explicit close-to-defining equations.

(b) The explicit varieties in the theorem establishing black-box derandomization of symbolic determinant identity testing have explicit defining equations.

These assertions concern the construction of equations for explicit varieties, a central obstacle in geometric complexity theory; the source gives no resolution.

Sources & referencesView supporting material

Primary source

Ketan D. Mulmuley, “Geometric Complexity Theory V: Efficient algorithms for Noether Normalization”, arXiv:1209.5993 (2016).

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