David Swinarski

Gröbner Techniques for Low-Degree Hilbert Stability

We give a method for verifying, by a symbolic calculation, the stability or semistability with respect to a linearization of fixed, possibly small, degree m, of the Hilbert point of a scheme having a suitably large automorphism group. We also implement our method and apply it to analyze the stability of bicanonical models of certain curves. Our examples are very special, but they arise naturally in the log minimal model program for . In some examples, this connection provides a check of our computations; in others, the computations confirm predictions about conjectural stages of the program.

PD-L1 expression in non-small cell lung carcinoma: Comparison among cytology, small biopsy, and surgical resection specimens: PD-L1 Expression in NSCLC Specimens

One immunotherapeutic agent for patients with advanced non‐small cell lung carcinoma, pembrolizumab, has a companion immunohistochemistry (IHC)‐based assay that predicts response by quantifying programmed death‐ligand 1 (PD‐L1) expression. The current study assessed the feasibility of quantifying PD‐L1 expression using cytologic non‐small cell lung carcinoma specimens and compared the results with those from small biopsy and surgical resection specimens.

A Geometric Invariant Theory Construction of Moduli Spaces of Stable Maps

We construct the moduli spaces of stable maps, Graphic, via geometric invariant theory (GIT). This construction is only valid over Graphic, but a special case is a GIT presentation of the moduli space of stable curves of genus g with n marked points, Graphic; this is valid over Graphic. In another paper by the first author, a small part of the argument is replaced, making the result valid in far greater generality. Our method follows the one used in the case n = 0 by Gieseker in [9], 1982, Lectures on Moduli of Curves to construct Graphic, though our proof that the semistable set is nonempty is entirely different.

GIT stability of weighted pointed curves

In the late 1970s Mumford established Chow stability of smooth unpointed genus g curves embedded by complete linear systems of degree d ≥ 2g + 1, and at about the same time Gieseker established asymptotic Hilbert stability (that is, stability of m th Hilbert points for some large values of m) under the same hypotheses. Both of them then use an indirect argument to show that nodal Deligne-Mumford stable curves are GIT stable. The case of marked points lay untouched until 2006, when Elizabeth Baldwin proved that pointed Deligne-Mumford stable curves are asymptotically Hilbert stable. (Actually, she proved this for stable maps, which includes stable curves as a special case.) Her argument is a delicate induction on g and the number of marked points n; elliptic tails are glued to the marked points one by one, ultimately relating stability of an n-pointed genus g curve to Gieseker’s result for genus g + n unpointed curves. There are three ways one might wish to improve upon Baldwin’s results. First, one might wish to construct moduli spaces of weighted pointed curves or maps; it appears that Baldwin’s proof can accommodate some, but not all, sets of weights. Second, one might wish to study Hilbert stability for small values of m; since Baldwin’s proof uses Gieseker’s proof as the base case, it is not easy to see how it could be modified to yield an approach for small m. Finally, the Minimal Model Program for moduli spaces of curves has generated interest in GIT for 2, 3, or 4-canonical linear systems; due to its use of elliptic tails, Baldwin’s proof cannot be used to study these, as elliptic tails are known to be GIT unstable in these cases. In this paper I give a direct proof that smooth curves with distinct weighted marked points are asymptotically Hilbert stable with respect to a wide range of parameter spaces and linearizations. Some of these yield the (coarse) moduli space of Deligne-Mumford stable pointed curves M g,n and Hassett’s moduli spaces of weighted pointed curves M g,A, while other linearizations may give other quotients which are birational to these and which may admit interpretations as moduli spaces. The full construction of the moduli spaces is not contained in this paper, only the proof that smooth curves with distinct weighted marked points are stable, which is the key new result needed for the construction. For this I follow Gieseker’s approach to reduce to the GIT problem to a combinatorial problem, though the solution is very different.

Molecular testing on endobronchial ultrasound (EBUS) fine needle aspirates (FNA): Impact of triage

Endobronchial ultrasound (EBUS)‐guided fine needle aspiration (FNA) is performed to diagnose and stage lung cancer. Multiple studies have described the value of Rapid On‐Site Evaluation (ROSE), but often the emphasis is upon diagnosis than adequacy for molecular testing (MT). The aim was to identify variable(s), especially cytology‐related, that can improve MT.

Toward GIT stability of syzygies of canonical curves

We introduce the problem of GIT stability for syzygy points of canonical curves with a view toward a GIT construction of the canonical model of Mg. As the rst step in this direction, we prove the semi-stability of the rst syzygy point for a general canonical

Can you play a fair game of craps with a loaded pair of dice

Abstract The parts-to-totals map sends the distributions of a set of independent random variables on a finite set of probability spaces to the total distribution of their sum on the product space. We study, in special cases modeled by dice, the geometry of the extension to complex pseudoprobabilities of this map, arithmetic questions about the existence of real points in certain fibers, and, when these exist, of strict points, having all coordinates in the unit interval.

Nef divisors on

We construct, on a supersingular K3 surface with Artin invariant 1 in characteristic 2, a set of 21 disjoint smooth rational curves and another set of 21 disjoint smooth rational curves such that each curve in one set intersects exactly 5 curves from the other set with multiplicity 1 by using the structure of a generalized Kummer surface.We show that a family of minimal surfaces of general type with p_g = 0, K^2=7, constructed by Inoue in 1994, is indeed a connected component of the moduli space: indeed that any surface which is homotopically equivalent to an Inoue surface belongs to the Inoue family. The ideas used in order to show this result motivate us to give a new definition of varieties, which we propose to call Inoue-type manifolds: these are obtained as quotients \hat{X} / G, where \hat{X} is an ample divisor in a K(\Gamma, 1) projective manifold Z, and G is a finite group acting freely on \hat{X} . For these type of manifolds we prove a similar theorem to the above, even if weaker, that manifolds homotopically equivalent to Inoue-type manifolds are again Inoue-type manifolds.We give a simple proof of the non-rationality of the Fano threefold defined by the equations \Sigma x_i = \Sigma x_i^2 = \Sigma x_i^3 = 0 in P^6 .We compute the cohomology of the moduli stack of coherent sheaves on a curve and find that it is a free graded algebra on infinitely many generators.The divisors on

\M_{0,n}

\bar{\operatorname{M}}_g

from GIT

that arise as the pullbacks of ample divisors along any extension of the Torelli map to any toroidal compactification of