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This question is part II of my proof reading of Lemma of devissage from Mumford's & Oda's Algebraic Geometry II, findable on page 81; Theorem 6.12: Theorem 6.12 (“Lemma of devissage”). Let $K$ b …

I have a question about an argument on $m$-regularity from 'Fundamental Algebraic Geometry' by Fantechi on page 114, Chapter 5.2: Castelnovo-Mumford regularity. The statement is: Let $k$ be a field a …

supplement/ an "almost" answer: I noticed that OP's of several related questions (1, 2) asked about similar issue. The best explanation I found there was that for a smooth manifold $X$ the tangent spa …

Let $f: X \to Y$ be a separated morphism between $k$-varieties or more general schemes of finite type. The most common way in standard literature on algebraic geometry to define the sheaf of relative …

I have a question about a step in the proof of the Existence of Flattening Stratification I found in Nitsure's paper here: https://arxiv.org/abs/math/0504590 This question is closely related to Local …

I study Nitin Nitsures paper on the Construction of Hilbert and Quot Schemes and not understand the propetry (F) completely: In previous chapter (Embedding Quot into Grassmanian) it was proved that t …

In 'Fundamental Algebraic Geometry' by Fantechi there is a lemma in section 5.3.2, page 119: LEMMA 5.5 Let $S$ be a noetherian scheme and let $F$ be a coherent sheaf on $\mathbb{P}^n_S$. Suppose there …

I'm reading Mumfords's Lectures on Curves on an Algebraic Surface (jstor-link: https://www.jstor.org/stable/j.ctt1b9x2g3) and I found in Lecture 7 (RESUME OF THE COHOMOLOGY OF COHERENT SHEAVES ON $\ma …