# atricolf

Italy

I am a graduate student working in Algebraic Geometry. My main interest is in moduli of curves, their intersection theory and cohomology.

 May 18 asked How many smoothings are there for a nodal curve? May 7 awarded Caucus Apr 26 accepted The analytic and the algebraic "small disc" Apr 26 comment The analytic and the algebraic "small disc"Dear @Andrew, your answer is great. Thank you very much! Apr 26 comment The analytic and the algebraic "small disc"Dear @PiotrPstragowski, thanks for your comments; understanding the correspondence between completion and "taking infinitesimal neighborhood" was exactly the aim of my question :) Apr 26 comment The analytic and the algebraic "small disc":thank you for your answer. In what sense can I view the generic fiber (which is one fiber) as a "family", as you wrote? Apr 23 comment Why is an intersection product $X.C=0$?You are perfectly right. Linear equivalence has nothing to do with the kernel of the intersection pairing. Thank you! Apr 23 asked The analytic and the algebraic "small disc" Apr 23 asked Why is an intersection product $X.C=0$? Apr 19 accepted Blowing up a line $L\subset \mathbb A^3$ Apr 19 comment Blowing up a line $L\subset \mathbb A^3$Dear @Andrew, thank you for all your explanations. I should look again at "The Geometry of Schemes", where I read about this approach some time ago... Apr 18 comment Blowing up a line $L\subset \mathbb A^3$Thank you, @Andrew. I find your first paragraph very clear, but the second one remains a bit obscure to me. For instance why is it fine to consider $R_1$ and $R_2$ defined that way? (i.e. why do we look at $f_i/f_j$?) Apr 17 asked Blowing up a line $L\subset \mathbb A^3$ Apr 14 awarded Yearling Apr 14 awarded Yearling Apr 13 comment Möbius strip and $\mathscr O(-1)$. Or $\mathscr O(1)$?@GeorgesElencwajg: thank you very much for correcting your answer. I really appreciate it. Apr 13 comment Number of lines passing through a fixed point in a quadric surface@MichaelJoyce: thank you! and... just one line defined over the base field is an impossible situation, right? Apr 12 comment Number of lines passing through a fixed point in a quadric surfaceSo are there at most $2$ lines, or exactly $2$ lines? Does this depend on the base field? Thank you! Apr 12 answered Reference request: Projective space $\mathbb{RP}^3$ Apr 11 comment Is $\{x\in R\mid A \cap Rx=\emptyset\text{ and }A \cap xR=\emptyset\}$ infinite in a ring?In $B$, do you mean $\emptyset$ (as you wrote) or $0$? Because whatever $A$ you choose, $B=\emptyset$ ($0\in xR$).