On the field intersection problem of quartic generic polynomials via formal Tschirnhausen transformation

Let $k$ be a field of characteristic $\neq 2$. We give an answer to the field intersection problem of quartic generic polynomials over $k$ via formal Tschirnhausen transformation and multi-resolvent polynomials.Comment: 32 pages, 6 tables, to appear in Comment. Math. Univ. St. Paul