special assessments and cost basis

No.  If you sold it for 100,000 and your cost basis is 50,000 your gain is 50,000.  If you add 10,000 to the cost basis then your cost is 60,000 and the gain is reduced to 40,000 (100,000-60,000).  The capital gain is the profit.  

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@Brigantine117 wrote:
If I'm increasing my cost basis by adding the assessment, wouldn't that increase my capital gain?

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No, it would serve to decrease your capital gain when you sell your property.

Example:

Purchase price: $100,000 = Cost basis

Special Assessment: $10,000

Adjusted basis = $110,000 (cost basis plus special assessment)

Sales price: $150,000

Gain: $40,000 (Sales price of $150,000 less $110,000 adjusted basis)