# Angelo

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## Registered User

 Name Angelo Member for 3 years Seen 2 hours ago Website Location Italy Age 54
My name is Angelo Vistoli. I do algebraic geometry, mostly moduli theory.

Normally I don't answer questions from anonymous users.
 2h comment When is the intersection of an isolated normal singularity with a generic linear subspace through that singularity normal?Actually, the way the question was formulated so that the intersection has dimension 2. In this case, to get a positive answer you need the singularity to be Cohen-Macaulay. 7h comment Finitely-generated abelian groupIf you can't do your homework problems, I would suggest, first of all, studying, and, if this fails, going to your teacher's office hours. 8h comment Embedded associated prime and non zero divisorIf you can't do your homework problems, I would suggest, first of all, studying, and, if this fails, going to your teacher's office hours. I voted to close. 18h accepted When is the intersection of an isolated normal singularity with a generic linear subspace through that singularity normal? 19h answered When is the intersection of an isolated normal singularity with a generic linear subspace through that singularity normal? 1d comment Differential form on a compact manifold whose exterior derivative is nowhere zero?Obviously it does not vanish anywhere on $\mathbb R^3$, but you are restricting it to $S^2$, and the restriction map is not pointwise injective. I voted to close as "too localized". 1d accepted Homological characterization of smooth maps 1d answered Homological characterization of smooth maps May17 revised Rigidification and good moduli space (morphism) in the sense of Alperdeleted 7 characters in body May15 accepted Rigidification and good moduli space (morphism) in the sense of Alper May15 answered Rigidification and good moduli space (morphism) in the sense of Alper May14 comment Flatness over Jacboson ringNo. Take $A = k[x,y]$, and as $M$ the quotient field of $k[x] = k[x,y]/(y)$. May12 comment Simple automorphism groups of field extensions of infinite transcendence degreeI suppose you want $k$ to be also algebraically closed, otherwise the subgroup of elements fixing $\overline k \subseteq K$ would be a proper normal subgroup. I don't have access to Lascar's paper, but from the title I would guess he takes $k = \overline{\mathbb Q}$. May12 comment Proving that a generic variety with ample canonical bundle has no automorphismsI meant this: it is very hard to imagine this might be true, but if it were, it would probably be extremely difficult to prove. In any case, it seems that you are being given counterexamples. May12 comment Proving that a generic variety with ample canonical bundle has no automorphismsYou want to do this for every possible family? That is very hard to imagine. May9 comment Etale Cohomology of Punctured Spectra of Local RingsThe algebraic cohomology of $\mathbb G_{\rm m}$ is very different from the analytic cohomology of $\mathcal O^*$. For a regular scheme the former is always torsion in degree at least 2 (this is a well-known result of Grothendieck), whereas the analytic cohomology of a complex manifold tends to contain positive-dimensional $\mathbb Q$-vector spaces. May7 comment IGP for non-fixed ground fieldPlease read the FAQ. May5 comment IGP for non-fixed ground fieldThe proof is fine, but the question is off-topic. May4 comment How to show an ideal is Zero-dimensionalThis sounds like a homework problem. I voted to close. May1 comment Dense Affine Subvarieties of Algebraic VarietiesThis must be done a little more carefully: the union is not necessarily affine, or even a subvariety. Apr30 comment Uniqueness of deformation family, A first order deformation extends to a miniversal deformation if and only if the corresponding Kodaira-Spencer map is an isomorphism. Your modified deformation obviously satisfies this condition. Then you use uniqueness of miniversal deformations. Apr29 comment Uniqueness of deformation family, What do you mean by an isomorphism of deformations? If the isomorphism is supposed to be over $T$, then the answer is negative, because the two families have different Kodaira-Spencer maps. If, on the other hand, you allow automorphisms of $T$, the answer should be positive for trivial reasons. Apr29 comment Zariski’s main theorem in the form of Grothendieck, universal propertiesI guess that "Galois with group $G$" should not be interpreted as being necessarily étale. Anyway, it seems to me that (2) and (3) follows immediately from (1), personally I would not worry with a reference. Of course, I am not very good with references. Apr27 comment Tangent space in Algebraic geometry and Differential geometryCan't you work out an example before asking a question? How can you think that the intersection of all curves with a given tangent vector is 1-dimensional? Apr26 comment canonical model of a reducible curveThe canonical sheaf of a stable curve with an elliptic tale is not globally generated. Apr25 accepted Can Inequivalent Topologies Have Same Sheaves/Cohomology? Apr24 comment Relation of degree and genus of superelliptic curvesAll this follows easily from Riemann-Hurwitz. Apr24 answered Can Inequivalent Topologies Have Same Sheaves/Cohomology? Apr20 comment Kawamata-Viehweg Vanishing Theorem for Excellent Surfaces It follows easily from the fact that a finitely dimensional algebra is Jacobson; in particular, the closed points are dense. So, if there is only one closed point, the spectrum consists of that point, so the algebra is 0-dimensional, hence artinian. Apr20 comment Kawamata-Viehweg Vanishing Theorem for Excellent Surfaces No, a localization is practically never finitely generated. The local rings that are of finite type over a field are artinian. Apr20 comment Kawamata-Viehweg Vanishing Theorem for Excellent Surfaces Since the usual version of the Kawamata-Viehweg vanishing theorem generalized Kodaira's, you'd better write down the exact statement that you need. Apr20 comment pushforward of injective sheaf acyclic for cohomology with supportsIt seems to the me that the étale case should reduced to the Zariski case, because the pushforward from the étale site to the Zariski site is also flabby. Am I missing something? Apr19 comment Kawamata-Viehweg Vanishing Theorem for Excellent Surfaces Doesn't Kodaira vanishing fail for surfaces in positive characteristic? Raynaud gave counterexamples. Apr18 comment Is there a picture I should have in my head of rational homotopy equivalence? Wasn't it Von Neumann who said that in mathematics you don't understand things, you just get used to them? Apr18 comment Is there an elliptic surface over $Y(1)$?Will Sawin's answer is correct. Apr16 comment What is “Data” involved in a mathematical construction?You would like to be notified in advance? Apr15 accepted Semiring of algebraic vector bundles on projective space Apr15 answered What is “Data” involved in a mathematical construction? Apr14 comment on flat morphismsWhy the heck should it imply that $f$ is flat? Did you forget a hypothesis? Apr14 comment Localization sequence for K^0(X)link.springer.com/chapter/… Apr13 comment A question about fiberbundles in algebraic geometryLocally trivial meaning locally a product? This is an extremely restrictive notion; usually one uses the étale topology. Also, if you want an analogue of the topological notion of fiber bundle even having isomorphic fibers may be too strong. For example, a smooth projective morphism is topologically a fiber bundle, but does not have isomorphic fibers in general. Apr10 answered Weil restriction of abelian schemes along finite étale (resp. finite locally free) morphisms Apr9 accepted Can one pick generators for the ring of invariants of binary n-ic forms which have rational coefficients? Apr9 answered Can one pick generators for the ring of invariants of binary n-ic forms which have rational coefficients? Apr7 revised The sum of same powers of all matrices modulo pdeleted 508 characters in body; deleted 7 characters in body Apr7 answered The sum of same powers of all matrices modulo p Apr6 awarded ● Nice Answer Apr6 revised How to refer to a theorem that you have shown to be wrongdeleted 2 characters in body Apr5 answered How to refer to a theorem that you have shown to be wrong Apr4 accepted Finite-type Artin Stack over $\mathbb C$