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There is an operation in algebraic geometry, called a flip, which is a (kind of a special) surgery, so one could say that you hear about it, but under a different name. You can see the definition of a flip on page 41 of Birational geometry of algebraic varieties by János Kollár and Shigefumi Mori (unfortunately that exact page is not available on google books). See also this and this MO answers.

One possible reason for the general lack of mentioning surgery in general may be that it is extremely hard to prove that it exists (at least for flips, but I suppose if one came up with a more general definition it would be also hard to prove existence). Shigefumi Mori was awarded the Fields Medal for proving the existence of flips in dimension 3 and it was only proved very recently by Hacon and McKernan that flips exist in any dimension. (Of course, here one would have to mention the works of Shokurov and Siu that influenced them and give references and try to give credit to everyone, but I don't want to write a book here, so let me just leave researching this in detail for the reader for now.)

There is an operation in algebraic geometry, called a flip, which is a (kind of a special) surgery, so one could say that you hear about it, but under a different name. You can see the definition of a flip on page 41 of Birational geometry of algebraic varieties by János Kollár and Shigefumi Mori (unfortunately that exact page is not available on google books). See also this and this MO answers.

One possible reason for the general lack of mentioning surgery in general may be that it is extremely hard to prove that it exists (at least for flips, but I suppose if one came up with a more general definition it would be also hard to prove existence). Shigefumi Mori was awarded the Fields Medal for proving the existence of flips in dimension 3 and it was only proved very recently by Hacon and McKernan that flips exist in any dimension. (Of course, here one would have to mention the works of Shokurov and Siu that influenced them and give references and try to give credit to everyone, but I don't want to write a book here, so let me just leave researching this in detail for the reader for now.)

There is an operation in algebraic geometry, called a flip, which is (supposed to be) a surgery, so one could say that you hear about it, but under a different name. You can see the definition of a flip on page 41 of Birational geometry of algebraic varieties by János Kollár and Shigefumi Mori (unfortunately that exact page is not available on google books). See also this MO question/answer.

One possible reason for the general lack of mentioning surgery in general may be that it is extremely hard to prove that it exists (at least for flips, but I suppose if one came up with a more general definition it would be also hard to prove existence). Shigefumi Mori was awarded the Fields Medal for proving the existence of flips in dimension 3 and it was only proved very recently by Hacon and McKernan that flips exist in any dimension. (Of course, here one would have to mention the works of Shokurov and Siu that influenced them and give references and try to give credit to everyone, but I don't want to write a book here, so let me just leave researching this in detail for the reader for now.)

There is an operation in algebraic geometry, called a flip, which is a (kind of a special) surgery, so one could say that you hear about it, but under a different name. You can see the definition of a flip on page 41 of Birational geometry of algebraic varieties by János Kollár and Shigefumi Mori (unfortunately that exact page is not available on google books). See also this and this MO answers.

One possible reason for the general lack of mentioning surgery in general may be that it is extremely hard to prove that it exists (at least for flips, but I suppose if one came up with a more general definition it would be also hard to prove existence). Shigefumi Mori was awarded the Fields Medal for proving the existence of flips in dimension 3 and it was only proved very recently by Hacon and McKernan that flips exist in any dimension. (Of course, here one would have to mention the works of Shokurov and Siu that influenced them and give references and try to give credit to everyone, but I don't want to write a book here, so let me just leave researching this in detail for the reader for now.)

There is an operation in algebraic geometry, called a flip, which is (supposed to be) a surgery, so one could say that you hear about it, but under a different name. You can see the definition of a flip on page 41 of Birational geometry of algebraic varieties by János Kollár and Shigefumi Mori (unfortunately that exact page is not available on google books).

One possible reason for the general lack of mentioning surgery in general may be that it is extremely hard to prove that it exists (at least for flips, but I suppose if one came up with a more general definition it would be also hard to prove existence). Shigefumi Mori was awarded the Fields Medal for proving the existence of flips in dimension 3 and it was only proved very recently by Hacon and McKernan that flips exist in any dimension. (Of course, here one would have to mention the works of Shokurov and Siu that influenced them and give references and try to give credit to everyone, but I don't want to write a book here, so let me just leave researching this in detail for the reader for now.)

There is an operation in algebraic geometry, called a flip, which is (supposed to be) a surgery, so one could say that you hear about it, but under a different name. You can see the definition of a flip on page 41 of Birational geometry of algebraic varieties by János Kollár and Shigefumi Mori (unfortunately that exact page is not available on google books). See also this MO question/answer.

One possible reason for the general lack of mentioning surgery in general may be that it is extremely hard to prove that it exists (at least for flips, but I suppose if one came up with a more general definition it would be also hard to prove existence). Shigefumi Mori was awarded the Fields Medal for proving the existence of flips in dimension 3 and it was only proved very recently by Hacon and McKernan that flips exist in any dimension. (Of course, here one would have to mention the works of Shokurov and Siu that influenced them and give references and try to give credit to everyone, but I don't want to write a book here, so let me just leave researching this in detail for the reader for now.)