To obtain a polymer capable of forming a high-sensitivity and a high-resolution resist resin for a specific short-wavelength ArF laser excellent in process adaptability and useful in the ultrafine processing field of semiconductors by including a polyorganosilsesquioxane having a specific structure therein.

This polymer contains a compound represented by the formula [R1 and R2 are each a 1-4C alkyl or an ester decomposable with an acid; R3 to R6 are each a 1-4C alkyl or H; (n) is >0] and is obtained by carrying out a hydrolysis and condensation of, e.g. a 2-cyanoalkylalkoxysilane with an alkoxysilane having a 1-4C alkyl and a trialkoxysilane having an unsaturated functional group, simultaneously hydrolyzing a part of the cyano and then conducting an addition reaction of an acrylic or a methacrylic monomer having a group decomposable with the acid (e.g. t-butoxycarbonyl, t-butyl, tetrahtdropyranyl, trimethylsilyl or ethoxyethyl) in the presence of a radical initiator.