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bio website math.washington.edu/~kovacs
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I am an algebraic geometer.

Jul
1
revised The canonical bundle of an infinitesimal deformation
added 4 characters in body
Jul
1
comment The canonical bundle of an infinitesimal deformation
Right, of course. I guess I got stock in the proper world by the wording of the question... :)
Jun
30
answered The canonical bundle of an infinitesimal deformation
Jun
26
comment Morphisms contracting a family of curves
Hi Roy, this sounds good. It's a nice proof assuming that $Y$ is projective. The statement is still true assuming that $g$ is proper and $f$ is arbitrary (plus the connectivity assumptions). (Which is what I had in mind all along so I thought that there cannot be such a simple proof. But there is one with $Y$ projective). Cheers! :)
Jun
25
comment Morphisms contracting a family of curves
Roy: I am not sure how that works if you only know that a special fiber is contracted. In that case the general hyperplane section will miss the point where that special fiber maps and thus does not give any information. No?
Jun
25
answered Morphisms contracting a family of curves
Jun
12
revised is there a pattern here showing up or it's simply a coincidence?
added 1 character in body
Jun
11
revised Projective dimension of zero module
deleted 3 characters in body
Jun
2
awarded  Necromancer
May
28
awarded  Nice Answer
May
27
comment how does one understand GRR? (Grothendieck Riemann Roch)
@GregorBruns: You are absolutely correct, I left out a term (I had curves in my mind), but I now corrected it. Thanks for spotting the omission!
May
27
revised how does one understand GRR? (Grothendieck Riemann Roch)
corrected the exponential Chern character of L and the consequences of this correction.
May
26
comment On the number of irreducible components of an exceptional divisor
@JeskoHüttenhain:It's actually not surprising. Think about the case of a quadric cone and a ruling. If you blow up the line with the reduced scheme structure, you get the same as if you blew up the point, because it is not a Cartier divisor. But if you blow up the double line, then nothing happens, because you blew up a Cartier divisor. Similar things can happen if X is smooth, but Z is singular.
May
26
answered On the number of irreducible components of an exceptional divisor
May
6
comment Could we extend any line bundle on the smooth part of a singular curve to a line bundle on the whole curve?
On a curve a non-empty subset is open if and only if its complement is finite. $X_0$ contains the open subset $U_0$ and hence the complement of $X_0$ is contained in the complement of $U_0$, which is finite. OK?
May
4
answered Could we extend any line bundle on the smooth part of a singular curve to a line bundle on the whole curve?
Apr
28
comment Determine existence of irreducible variety in given homology class
Also, you would probably want to ask this differently. Say, not for a general homology class, but say a class in $\mathrm{Pic}\, X$. Otherwise, besides solving the Schottky problem you are also in danger of proving the Hodge Conjecture.
Apr
28
comment Simple example of a ring which is normal but not CM
@VA: Nice reference!
Apr
14
comment Cohen-Macaulayness of the direct image of the canonical sheaf
Just to extend on Karl's excellent answer: a slightly more general situation (that is, not just for $\omega_X$) is handled in Kollár's recent book (goo.gl/JE2CyM). Look at section 2.5.In particular, Theorem 2.74 gives exactly what Karl is saying with the substitution $\mathscr G=\omega_X$.
Apr
12
answered Question about a divisor and its image